Yes, but Oblivion is ridiculously processor-intensive, as well as GPU-intensive (and by extension, PSU-intensive). I don't know what these handhelds have in terms of GHz, but 3.0+ GHz is recommended for Oblivion.
The PSP version of Oblivion was never intended to be the same as the version released for PC/360/PS3. The PSP version didn't have any outdoor areas, it was a dungeon crawler with 10 large levels and used new art for the graphics, which looked quite good too. Sort of like Battlespire but with the Oblivion storyline, I guess.
Not that it matters though, the game development of the PSP version was cancelled long ago. The developer studio gamesas hired to make the game was shut down.