I listened to this Charice girl, and I highly doubt she'd become very successful in North America.
Here's why according to me:
Yes, she has a very good voice, but it's nothing special. Like someone else said - she sounds a bit like Christina Aguilera. There are many many female vocalists in North America now who have the same vocal quality as she does, and there isn't really the need for another. So she doesn't stand out vocally.
Also, I hate to say this, she's not very pretty. Even with a lot of make-up, she still looks very plain and probably won't be able to compete with the much prettier singers here.
Another thing is, she doesn't strike me as someone charming (and this is different than just her physical appearance). Her performance seems very stiff - her movements and her song are not integrated well, and seem forced and awkward. If you don't have the charms or personality, people may not be as willing to pay money and see you perform, and a lot of singers depend on tours to make money.
In the end, if she does make it - good for her. She does have a very good voice. But is it special enough, and does she have the looks and personality? I'm not too sure.