Q:

1st Thessalonians 4:13-14: "those who sleep in Jesus"

Is there any possibility that "those who sleep in Jesus" that Paul is talking about in 1st Thessalonians 4:13-14 are the believers from the Old Testament that had never heard of Jesus?:  

But I would not have you to be ignorant, brethren, concerning them
  which are asleep, that ye sorrow not, even as others which have no
  hope.  For if we believe that Jesus died and rose again, even so them
  also which sleep in Jesus will God bring with him. ( 1Th.  4:13-14, KJV)

A:

The Greek text of the Textus Receptus (Estienne, 1550) states,

εἰ γὰρ πιστεύομεν ὅτι Ἰησοῦς ἀπέθανεν καὶ ἀνέστη οὕτως καὶ ὁ θεὸς τοὺς κοιμηθέντας διὰ τοῦ Ἰησοῦ ἄξει σὺν αὐτῷ

The majority of the English translation of the Greek is straightforward. 

For if we believe that Jesus died and resurrected, likewise God will bring those asleep [διὰ τοῦ Ἰησοῦ] with him. 

The Greek phrase in question is διὰ τοῦ Ἰησοῦ. The same phrase does not occur elsewhere in the Bible verbatim.  However, similar phrases do occur frequently elsewhere with the Lord Jesus Christ as the object of the preposition διά.
For example:

Rom.  5:1 - διὰ τοῦ κυρίου ἡμῶν Ἰησοῦ Χριστοῦ ("by* our Lord Jesus Christ")
Rom.  5:11 - διὰ τοῦ κυρίου ἡμῶν Ἰησοῦ Χριστοῦ ("by* our Lord Jesus Christ")
Rom.  5:17 - διὰ τοῦ ἑνὸς Ἰησοῦ Χριστοῦ  ("by* one, Jesus Christ")
Rom.  5:21 - διὰ Ἰησοῦ Χριστοῦ τοῦ κυρίου ἡμῶν ("by* Jesus Christ our Lord")
Rom 7:25 - διὰ Ἰησοῦ Χριστοῦ τοῦ κυρίου ἡμῶν ("by* Jesus Christ our Lord")
Rom.  15:30 - διὰ τοῦ κυρίου ἡμῶν Ἰησοῦ Χριστοῦ ("by* our Lord Jesus Christ")
1 Cor.  15:57 - διὰ τοῦ κυρίου ἡμῶν Ἰησοῦ Χριστοῦ  ("by* our Lord Jesus Christ")
2 Cor.  5:18 - διὰ Ἰησοῦ Χριστοῦ ("by* Jesus Christ")
Gal.  1:1 - διὰ Ἰησοῦ Χριστοῦ ("by* Jesus Christ")
Eph.  1:5 - διὰ Ἰησοῦ Χριστοῦ ("by* Jesus Christ")
Eph.  3:9 - διὰ Ἰησοῦ Χριστοῦ ("by* Jesus Christ")
1 Thes.  4:2 - διὰ τοῦ κυρίου Ἰησοῦ  ("by* the Lord Jesus")
1 Thes.  5:9 - διὰ τοῦ κυρίου ἡμῶν Ἰησοῦ Χριστοῦ ("by* our Lord Jesus Christ")
2 Thes.  3:12 - διὰ τοῦ κυρίου ἡμῶν Ἰησοῦ Χριστου ("by* our Lord Jesus Christ")
Tit.  3:6 - διὰ Ἰησοῦ Χριστοῦ τοῦ σωτῆρος ἡμῶν ("by* Jesus Christ our savior")

Evidently, translating διὰ τοῦ Ἰησοῦ into English as "in Jesus" lacks precedent in the entire NT corpus.  According to Thayer, p. 134, the preposition διὰ followed by a noun in the genitive case is commonly used in the context

III.  of the Means or Instrument by which anything is effected; because what is done by means of a person or thing seems to pass as it were through the same [cf.  W. 378 (354)]. 

of one who is the author of the action as well as its instrument, or of the efficient cause: διʼ αὐτοῦ (i. e. τοῦ θεοῦ) τὰ πάντα sc.  ἐστίν or ἐγένετο, Ro.  11:36; also διʼ οὗ, Heb.  2:10; διʼ οὗ ἐκλήθητε, 1 Co. 1:9; add [Gal.  4:7 L T Tr WH, see below]; Heb.  7:21 (ἡ ἰατρικὴ πᾶσα διὰ τοῦ θεοῦ τούτου, i. e. Aesculapius, κυβερνᾶται, Plat.  symp.  p. 186 e.; cf.  Fritzsche on Rom.  vol.  i. p. 15, [and for exx.  Soph.  Lex.  s. v. 1]); of him to whom that is due which any one has or has done; hence i. q. by the fault of any one: διʼ οὗ τὸ σκάνδαλον ἔρχεται, Mt. 18:7; διʼ ἑνὸς ἀνθρ.  ἡ ἁμαρτία … εἰσῆλθε, Ro.  5:12, cf.  16–19; ἠσθένει διὰ τῆς σαρκός, Ro.  8:3; by the merit, aid, favor of any one: ἐν ζωῇ βασιλεύσουσι διά etc.  Ro.  5:17, cf.18 sq.;  1 Co. 15:21; διὰ τοῦ Χριστοῦ, and the like: Ro.  5:1 sq.  11; Acts 10:43; Gal.  4:7 [Rec.,  but see above]; δοξάζειν τ.  θεὸν διὰ Ἰησοῦ Χριστοῦ, 1 Pet.  4:11, and εὐχαριστεῖν τῷ θεῷ διὰ Ἰησ.  Χρ.  Ro.  1:8; 7:25 (where L T Tr WH txt.  χάρις τῷ θεῷ); Col.  3:17,—because the possibility both of glorifying God and of giving thanks to him is due to the kindness of Christ; καυχᾶσθαι ἐν τῷ θεῷ διὰ Ἰησ.  Χρ.  Ro.  5:11; ἀναπαύεσθαι διά τινος, Philem.  7; οἱ πεπιστευκότες διὰ τῆς χάριτος, Acts 18:27; πολλῆς εἰρήνης τυγχάνοντες διὰ σοῦ … διὰ τῆς σῆς προνοίας, Acts 24:2 (3); ὑπερνικᾶν διὰ τοῦ ἀγαπήσαντος ἡμᾶς, Ro.  8:37; περισσεύειν διά τινος, by the increase which comes from one, Phil.  1:26; 2 Co. 1:5; 9:12; διὰ τῆς ὑμῶν δεήσεως, Phil.  1:19; add, Philem.  22; Ro.  1:12; 2 Co. 1:4; Gal.  4:23; 1 Pet.  1:5. 

of the instrument used to accomplish a thing, or of the instrumental cause in the stricter sense:—with gen.  of pers.  by the service, the intervention of, any one; with gen.  of thing, by means of, with the help of, any thing;

a. in passages where a subject expressly mentioned is said to do or to have done a thing by some person or by some thing: Mk.  16:20 (τοῦ κυρίου τὸν λόγον βεβαιοῦντος διὰ τ.  σημείων); Lk.  1:70; Acts 1:16; 2:22 (τέρασι κ.  σημείοις, οἷς ἐποίησε διʼ αὐτοῦ ὁ θεός); 8:20; 10:36; 15:23 (γράψαντες διὰ χειρὸς αὐτῶν); 20:28; 21:19; 28:25; Ro.  2:16; 3:31; 7:13; [8:11 Rec.  bez elz L ed.  min.  T WH txt.];  15:18; 16:1]; 15:18; 16:18; 1 Co. 1:21 [cf.  W. 381 (357)]; 2:10; 4:15; 6:14; 14:9, 19 [R G]; 15:57; 2 Co. 1:4; 4:14 R G; 5:18, 20; 9:13 [cf.  W. 381 (357)]; 10:9; 12:17; Eph.  1:5; 2:16; Col.  1:20, 22; 2:8; 1 Th.  4:14; 2 Th.  2:14; Tit.  3:5; Heb.  1:2, 3 [R G]; 2:14; 6:12; 7:19; 9:26; 13:2, 12, 15, 21; Rev. 1:1; γῆ ἐξ ὕδατος (material cause) κ.  διʼ ὕδατος συνεστῶσα τῷ τοῦ θεοῦ λόγῳ, 2 Pet.  3:5 [W. 419 (390) cf.  217 (204)]. 

In his commentary on 1 Thes.  4:14, Heinrich Meyer states,

We are accordingly constrained to unite διὰ τοῦ Ἰησοῦ  with ἄξει. 

If indeed διὰ τοῦ Ἰησοῦ should be translated as "by Jesus," how is it understood in relation to the rest of the clause? 

For if we believe that Jesus died and resurrected, likewise God will bring those asleep by Jesus (διὰ τοῦ Ἰησοῦ) with him. 
εἰ γὰρ πιστεύομεν ὅτι Ἰησοῦς ἀπέθανεν καὶ ἀνέστη οὕτως καὶ ὁ θεὸς τοὺς κοιμηθέντας διὰ τοῦ Ἰησοῦ ἄξει σὺν αὐτῷ

Recall that the Thessalonians were mourning over their dead Christian brothers (1 Thes.  4:13), i.e. those asleep (τοὺς κοιμηθέντας).  The apostle Paul comforts them by saying that "if we believe that Jesus died and resurrected," well, God will likewise bring "those asleep" with him. 
Where will God bring the dead Christians from?  Since they are alseep (dead) in the grave, and the apostle Paul’s emphasis was on the fact that Jesus died and resurrected, evidently God will bring the dead Christians from the grave by resurrecting them, just as Jesus was brought from the dead when he was resurrected by God the Father. 
In Heb.  13:20, it is written,

But the God of peace who brought again from the dead our Lord Jesus, the great shepherd of the sheep, by the blood of the everlasting covenant
Ὁ δὲ θεὸς τῆς εἰρήνης ὁ ἀναγαγὼν ἐκ νεκρῶν τὸν ποιμένα τῶν προβάτων τὸν μέγαν ἐν αἵματι διαθήκης αἰωνίου τὸν κύριον ἡμῶν Ἰησοῦν

Notice the word ἀναγαγὼν which is a conjugation of the lemma ἀνάγω, which itself is composed of the prefix ἀν- meaning “again,” and the verb ἄγω, the same lemma found in 1 Thes.  4:14. 

God brought Jesus from the dead when he resurrected him (Heb.  13:20). 
God [the Father] gave Jesus the authority to resurrect the dead on the last day (John 6:39-40). 
God will bring dead Christians from the dead by resurrecting them, just as he resurrected Jesus from the dead (hence, οὕτως καὶ or "likewise"). 
However, God will resurrect the dead Christians by Jesus (διὰ τοῦ Ἰησοῦ). 
Hence, God will bring them from the dead with Jesus (ἄξει σὺν αὐτῷ). 

Dead Christians are brought from the dead. 
Dead Christians are brought from the dead with Jesus (albeit not simultaneously, but in order, and in time). 
Dead Christians are brought from the dead by Jesus (he is the means). 
It is certainly an awkward clause, but it is certainly more plausible than translating διὰ τοῦ Ἰησοῦ as "in Jesus." 
In conclusion, it seems more reasonable to interpret τοὺς κοιμηθέντας ("those asleep") as being the deceased loved ones of the Thessalonians, the very deceased that they were mourning for (cp.  1 Thes.  4:13).  From our own experiences, we don't mourn much if any for the Old Testament saints.  But, we certainly mourn whenever we lose a loved one, family or friend, even if we realize that they are Christians and will be resurrected in the future.  The death of loved ones always hurts. 
Footnotes
*"by/by means of/through" (but never "in")
References
Meyer, Heinrich August Wilhelm.  Critical and Exegetical Handbook to the New Testament.  Trans.  Moore, John C.; Dickson, William P. New York: Funk & Wagnalls, 1889.