If I get predicted AAAand Uni of Manchester requires A*AAwould I still be able to apply and if in the real exams I get AAA will they still take me in.
You would be able to apply, yes. The question is whether you would be likely to receive an offer or not. For 2022 entry, they accepted 285 applicants - of the 4295 who applied. That would tend to suggest that the course is fairly popular and that you might not receive an offer. (Note that neither of the aforementioned numbers are the offers they made, as that number is harder to source.)
Applicants who receive an offer of A*AA but ultimately achieve AAA would appear to have a reasonable chance of being accepted, given that UniGuide says: "Most popular A-Levels studied (and grade achieved): History A, English Literature A, Law A". (source)
It does little harm to put them down as one of your five choices. Just make sure that you also apply some unis where you predicted grades meet or exceed their entry requirements.