No way. For me, canon matters and I consider Star Trek canon ended with the end of "Enterprise."
Nah. That particular "canon" ended, but there's no rule that says you can't start another "canon" . . . and another one a generation later. There's always room for a new variation on an old favorite. None of this stuff is set in stone.
You might just as well pretend that no more Tarzan movies were made after the Johnny Weismuller series ended . . . or that no Frankenstein movie made after 1948 is "canon."
Getting back OT, the Khan/Moriarity thing sounds plausible. Moriarity only made one or two appearances in the original Conan Doyle "canon." It was subsequent retellings that built him up into a major recurring character. (Ditto Irene Adler.)
I can see Khan going the same route . . . and I wouldn't be at all surprised to see the Borg turn up in some future iteration of TOS. They're too popular to leave on the shelf for long.