In DS9, Sisko calls the NCC-1701 the first Enterprise, which implies that the in-universe cannon most likely doesn’t include that ship. It was just an unused design for a previously existing Enterprise that was never written into the storyline.
It’s hard to say, though. Of course, the series has always broken its own cannon on various occasions, but ENT was as ridiculous as Frink’s Star Wars edits, only in a bad way.