I've seen some digital cameras use a USB-> RCA cable for video out, but they are just utilising the connections (USB is turned off, and it routes video/audio to the USB pins. Probably Vid, Left Audio, Right Audio and a shared ground)
This won't do anything unless 1) the PSP has been designed to pass out analogue video/audio directly onto the USB pins. 2) The cable itself has an inbuilt USB device that can interface with the PSP to clone the framebuffer. This would require drivers on the PSP firmware/OS (so design or homebrew) as well as a spectacularly small USB device and AV decoder in the USB plug. Given the price, that is not the case.
(1) is the only viable option here, and I did not think PSP's could do this - but I don't own one. There is PSP homebrew software that lets you clone the video onto the PC screen via USB - but that is a USB->USB cable, and they simply pass the framebuffer as data to the PC and let the PC decode the image.