In the U.S., I think AH-va would be difficult, given the overwhelming popularity of the AY-va pronunciation. As a mn, however, I don't think it would be a big deal.
It's hard for me to say how many Avas I've met because I don't know any of them very well. Between my son's daycare, my work, and our church, there are probably about 10 little Avas in my circle of acquaintance.
I really like
Ava quite a bit, and I'm not bothered by its popularity. I wouldn't use it just because there are so many similar names I love more, like
Eva,
Aviva, and
Maeve.