[Verizon Galaxy Note 3 Q&A, Help & Troubleshooting] ronjwright:
No go. I imported SecEmail_J.apk from Hyperdrive RLS 7 (MJE) to /system/app, and when I fixed permissions and rebooted, it FC'd. When I restored the original SecEmail_J.apk and rebooted again, I had to re-set up my one account that was attached to it.

Here was the logcat when the app FC'd:

E/AndroidRuntime( 9672): FATAL EXCEPTION: main
E/AndroidRuntime( 9672): Process: com.android.email, PID: 9672
E/AndroidRuntime( 9672): java.lang.RuntimeException: Unable to start activity ComponentInfo{com.android.email/com.android.email.activity.Welcome}: android.database.sqlite.SQLiteException: Can't downgrade database from version 2202 to 2113
E/AndroidRuntime( 9672):	at android.app.ActivityThread.performLaunchActivity(ActivityThread.java:2282)
E/AndroidRuntime( 9672):	at android.app.ActivityThread.handleLaunchActivity(ActivityThread.java:2340)
E/AndroidRuntime( 9672):	at android.app.ActivityThread.access$800(ActivityThread.java:157)
E/AndroidRuntime( 9672):	at android.app.ActivityThread$H.handleMessage(ActivityThread.java:1247)
E/AndroidRuntime( 9672):	at android.os.Handler.dispatchMessage(Handler.java:102)
E/AndroidRuntime( 9672):	at android.os.Looper.loop(Looper.java:157)
E/AndroidRuntime( 9672):	at android.app.ActivityThread.main(ActivityThread.java:5293)
E/AndroidRuntime( 9672):	at java.lang.reflect.Method.invokeNative(Native Method)
E/AndroidRuntime( 9672):	at java.lang.reflect.Method.invoke(Method.java:515)
E/AndroidRuntime( 9672):	at com.android.internal.os.ZygoteInit$MethodAndArgsCaller.run(ZygoteInit.java:1265)
E/AndroidRuntime( 9672):	at com.android.internal.os.ZygoteInit.main(ZygoteInit.java:1081)
E/AndroidRuntime( 9672):	at dalvik.system.NativeStart.main(Native Method)
E/AndroidRuntime( 9672): Caused by: android.database.sqlite.SQLiteException: Can't downgrade database from version 2202 to 2113
E/AndroidRuntime( 9672):	at android.database.sqlite.SQLiteOpenHelper.onDowngrade(SQLiteOpenHelper.java:361)
E/AndroidRuntime( 9672):	at android.database.sqlite.SQLiteOpenHelper.getDatabaseLocked(SQLiteOpenHelper.java:255)
E/AndroidRuntime( 9672):	at android.database.sqlite.SQLiteOpenHelper.getWritableDatabase(SQLiteOpenHelper.java:164)
E/AndroidRuntime( 9672):	at com.android.email.provider.EmailProvider.getDatabase(EmailProvider.java:889)
E/AndroidRuntime( 9672):	at com.android.email.provider.EmailProvider.applyBatch(EmailProvider.java:3299)
E/AndroidRuntime( 9672):	at android.content.ContentProvider$Transport.applyBatch(ContentProvider.java:260)
E/AndroidRuntime( 9672):	at android.content.ContentProviderClient.applyBatch(ContentProviderClient.java:377)
E/AndroidRuntime( 9672):	at android.content.ContentResolver.applyBatch(ContentResolver.java:1230)
E/AndroidRuntime( 9672):	at com.android.emailcommon.provider.EmailContent$Account.save(EmailContent.java:6725)
E/AndroidRuntime( 9672):	at com.android.email.AccountBackupRestore.doRestoreAccounts(AccountBackupRestore.java:462)
E/AndroidRuntime( 9672):	at com.android.email.AccountBackupRestore.restoreAccountsIfNeeded(AccountBackupRestore.java:106)
E/AndroidRuntime( 9672):	at com.android.email.activity.Welcome.onCreate(Welcome.java:280)
E/AndroidRuntime( 9672):	at android.app.Activity.performCreate(Activity.java:5389)
E/AndroidRuntime( 9672):	at android.app.Instrumentation.callActivityOnCreate(Instrumentation.java:1105)
E/AndroidRuntime( 9672):	at android.app.ActivityThread.performLaunchActivity(ActivityThread.java:2246)
E/AndroidRuntime( 9672):	... 11 more

Apparently, the old email app uses an old database format, and I have a feeling that this would require a non-trivial change to make it compatible with the newer database format.