I would think so, but I'm not sure.
In my experience though, PS3-to-PSVita remote play has been "ehh" - the PS3 just doesn't have enough juice dormant in the background to properly stream. Then again, I've only tried Shadow of the Colossus - maybe other games work better. The PSVita wasn't really designed to be the PS3's companion device, it was designed with the PS4 in mind - chances are that you'll get far better results with that system.
As for PSOne games, you might as well buy those on the PSVita itself, there's no real need to stream them.