Resistive touchscreens are used on virtually all PDAs as the primary input method. There are now quite a few GPS units that use 4.3" TFT LCD, with touchscreen.
And I have made use of it for a prototype product:
http://www.youtube.com/watch?v=uBQbJHUGiz4
To use a resistive touchscreen, you will require a controller -- more than just a A/D converters (like analog joysticks), as it needs to be able to apply a voltage across one axis while using an A/D to measure the other.
Often these controllers communicate with the CPU over a serial interface (SPI, IIC, UART, etc). At issue here is getting a controller into the PSP with the right interface, and getting the software working.
Another option is to create a small circuit that has the touchscreen controller and CPU. (I have not seen a *small* CPU with touchscreen controller builtin, but it may be out there). The CPU would get samples from the controller, and have two D/A converters generate a ratiometric voltage for the PSP's analog joystick port. The CPU could sense touch pressure, allowing you to for example wire it in parallel to one the PSP buttons.
I may be speaking out of complete ignorance, as I do not have any specs on the PSP's analog joystick port...
Regards,
Pete