Will it get PS2 games as officially made ports? Absolutely. It has everything you really need in terms of input mechanisms and it is significantly more powerful then PS2 was. I fully expect there will be ports and they will probably even be better then their originals.
But using a homebrew emulator (once homebrew becomes possible)? Nope. It might be plausible for someone to try and make or port a PS2 emulator for Vita but I still don't expect many if any commercial PS2 games will run at full speed or even at a tolerable frame rate in emulation on a Vita. It would be more of a tech demo then something that you could actually play games with.