[Suddo]

Extra Spell is one of those by RAW feats people don't allow, because wizards are already so OP.
Technically it wouldn't but the question is what are you worried about? The worst that could happen is that you would have to take the time and money to inscribe it which is pretty low all considering.

Edit: And if the questions is more "can the wizard" the answer is yes as the feat allows you to be able to cast and learn the spell. The only question becomes that you might have to take the effort to actually write it versus what normally happens when you level.