Yes, there is no reason why you can't have invisible braces.
A well done porcelain veneer will not lessen the strength of that tooth in any way. Even though you feel like you had part of your tooth removed, you also need to think about it that you have also had that portion replaced.
Make sure you talk with your cosmetic dentist before starting all of this. Typically, I would have the teeth moved first, then make the veneer. You will want to be careful that straightening the teeth doesn't make your veneer not match as well afterwards.
Web reference: https://www.scottgreenhalghdds.com