I bet not. I typically stick to those purchases when I play my PS3/Vita. Playing a PS1/PS2 classic is very simple. I could play my copy of Marvel vs Capcom 2, MVC:Origins, Castlevania Lament of Innocence, Vagrant Story, Threads of Fate, Front Mission 3, and the list continues.
I get a feeling like it’s all going to feel oddly redone. They’ve moved past that generation and backwards compatibility was not something they ever considered. It’s like a brand new ecosystem. The Vita took some of the success of the PSP (IMO had a better library of games). The PS3 shed some light on PS1 and PS2’s legacy and the PS5 is keeping up with the success of the PS4. I don’t see any signs of them combining both systems and pulling them into one. I’d be surprised if it did.