I think it could technically be just barely possible. The PS2 ports (God of War, Metal Gear Solid) are not completely rewritten games. They have an emulation engine that downgrades things to a level the Vita can handle, and the video content is compressed to save space. There are actually much better quality versions of the videos for God of War that can be used with the Vita version using Repatch.
While there may not be a way for perfect PS2 emulation to occur, theoretically, one could create a software-based emulator that would bottleneck content, such as what was done with the two collections I mentioned above.
If you want to get super technical about it, GoW Collection and MGS HD are basically emulations of emulations, since they're based on the PS3 collections, so that kinda emphasizes that it could theoretically be possible.
And the PS3 can emulate PS2 just fine. That's how they have the PS2 Classics for PS3, like Psychonauts. Same with PS4.
The specs for PS3 vs Vita are manageably different. If the PS3 can do it, then the Vita could do it with a little bit of help.
Sony knows how to do it, they just don't want to.