I don't think that there has been an official word yet on how this will work, but I've heard rumors that the emu will only run off of the ps3 through remote play (all the processing being done by the ps3)
However this sounds impractical to me because.. a main reason you buy the psp is to have portability and having to be nearby a console to emulate a game when you could just play it on the console anyway is stupid.
Now I think you will be able to do remote play with the ps1 games due to the backwards compatability but, I also think that there is/will be a PSone emu for the psp that can run completely by itself.
endgadget - Also of note is the announcement of a new digital distribution system (Hub?) allowing users to download “games and applications” directly to Memory Stick – an early use will be for downloading and playing PSone games (via new emulator) directly off your memory cards
I would think that^ would confirm that there is an emu that runs on the psp because It says straight off the memory stick and it's from endgadget.com which I assume is a reputable source