Forget the PSP.
I have PSP 3000, and I love it, but it just can't compare to a DSL and a GBA flashcart when it comes to GBA games.
On the DSL you get perfect compatibility and smoothness because of the built in native hardware.
On the PSP you get an "accetable" result.
If you have low expectations and you don't know any better, I guess a PSP would do it.
But for me not even my modern Laptop and VBA can do justice to the real thing, some games still are a little jerky or suffer from screen tearing/glitches, so how can a PSP be satisfactory when not even my PC with all the filters, bells and whistles can do ?
Also,during the years and after a lot of testing with various emulators and several commercial retro game collections such as Capcom reloaded, Atari and SNK, I concluded that the PSP screen is absolutely terrible for ANY retro purposes.
With a weird native resolution of 480 x 272, most retro system look too small when displayed at 1:1 in their native resolution, and too blurry when streched to fill the screen in 4:3 mode, and absolutely terrible in full widescreen.
The only emulator that looks alright for my ( admittedly ) picky taste, is actually the GB/GBC, as the original resolution was so small that the PSP can actually do a clean 2:1 !!!
So really, as much as I love the hardware, I wouldn't recommend anybody to purchase one solely based on emulators capabilities, let alone the fact that the homebrew scene has been technically dead for years.
Unless you don't have any other options, then I guess it would have to do it...
But with better alternatives out there, the many android based tablets, phones and portable systems ( GCW Zero and the likes ) with much better processors and screens, and since the OP seem to have already a DSL, I'd stay away from the PSP, even if I'd get one for free.