Yes I would expect it to be noted on a vetting but if it's not too bad and doesn't affect him/her too much I would expect them to pass a vetting but perhaps with an addtional note to the effect that yes they have a parrot mouth but the vet does not anticipate it being a problem..providing that is their opinion of course.
Mine has a slight parrot mouth that was noted at 5 stage vetting that he sailed through. It's never been an issue, I just make sure his teeth are checked every 6 months xx