They can indeed! Well, a modded one can. From my last rabbit hole dive I can tell ya that the Vita has the PSP hardware built in so it while I think it’s technically “emulating” the PSP it runs it like native cuz…well it is.

So yeah, from the Vita you can launch the PSP emulator and it will run and function just like the PSP. Legit just running its own software so you’d almost never know you were on a Vita!