I would guess this is possible. Like someone or multiple people have already said in this topic. All the rubber duck does is act like a keyboard. So if it is possible to directly control the PSP's USB input/output, all you would need to do is use the PSP's micro/mini USB port and connect to a USB port on a computer and have a piece of software on your PSP that will simulate a keyboard on the USB connection. Probably a little harder than it sounds tho.
I am no PSP OS expert, so I don't know how hard this would be. First few thoughts is native software, permissions and hardware. C or assembly is your language of choice I guess.