That's possible but unlikely. MTP as defined by Suzanne Sluizer and Jon Postel in RFC 772 in September 01980 https://datatracker.ietf.org/doc/html/rfc772 seems to have been where SMTP got that convention for ending the message:

> ...and considers all succeeding lines to be the message text. It is terminated by a line containing only a period, upon which a 250 completion reply is returned.

But in 01980 Unix had only been released outside of Bell Labs for five years and was only starting to support ARPANET connections (using NCP), so I wouldn't expect it to be very influential on ARPANET protocol design yet. I believe both Sluizer and Postel were using TOPS-20; the next year the two of them wrote RFC 786 about an interface used under TOPS-20 at ISI (Postel's institution, not sure if Sluizer was also there) between MTP and NIMAIL.

For some context, RFC 765, the June 01980 version of FTP, extensively discusses the TOPS-20 file structure, mentions NLS in passing, and mentions no other operating systems in that section at all. In another section, it discusses how different hardware typically handles ASCII:

> For example, NVT-ASCII has different data storage representations in different systems. PDP-10's generally store NVT-ASCII as five 7-bit ASCII characters, left-justified in a 36-bit word. 360's store NVT-ASCII as 8-bit EBCDIC codes. Multics stores NVT-ASCII as four 9-bit characters in a 36-bit word. It may be desirable to convert characters into the standard NVT-ASCII representation when transmitting text between dissimilar systems.

Note the complete absence of either of the hardware platforms Unix could run on in this list!

(Technically Multics is software, not hardware, but it only ever ran on a single hardware platform, which was built for it.)

RFC 771, Cerf and Postel's "mail transition plan", admits, "In the following, the discussion will be hoplessly [sic] TOPS20[sic]-oriented. We appologize [sic] to users of other systems, but we feel it is better to discuss examples we know than to attempt to be abstract."
RFC 773, Cerf's comments on the mail service transition plan, likewise mentions TOPS-20 but not Unix. RFC 775, from December 01980, is about Unix, and in particular, adding hierarchical directory support to FTP:

> BBN has installed and maintains the software of several DEC PDP-11s running the Unix operating system. Since Unix has a tree-like directory structure, in which directories are as easy to manipulate as ordinary files, we have found it convenient to expand the FTP servers on these machines to include commands which deal with the creation of directories. Since there are other hosts on the ARPA net which have tree-like directories, including Tops-20 and Multics, we have tried to make these commands as general as possible.

RFC 776 (January 01981) has the email addresses of everyone who was a contact person for an Internet Assigned Number, such as JHaverty@BBN-Unix, Hornig@MIT-Multics, and Mathis@SRI-KL (a KL-10 which I think was running TOPS-20). I think four of the hosts mentioned are Unix machines.

So, there was certainly contact between the Unix world and the internet world at that point, but the internet world was almost entirely non-Unix, and so tended to follow other cultural conventions. That's why, to this day, commands in SMTP and header lines in HTTP/1.1 are terminated by CRLF and not LF; why FTP and SMTP commands are all four letters long and case-insensitive; and why reply codes are three-digit hierarchical identifiers.

So I suspect the convention of terminating input with "." on a line of its own got into ed(1) and SMTP from a common ancestor.

I think Sluizer is still alive. (I suspect I met her around 01993, though I don't remember any details.) Maybe we could ask her.