TomTom firmware is closed-source, and distributing modified versions of it would likely be illegal. You could play with OpenTom, an open source firmware for TomTom, though. But there are some major problems with what you're proposing.
First, I think the TomTom runs on the ARM architecture. The PSP, like the PS2 before it, uses MIPS. Second, the GPS unit for the PSP interfaces with the console in a completely different way from how the TomTom's internal GPS unit works.
Then there's the TomTom's touch-screen. You'd have to code in some kind of cursor for tapping.
Tons of work. Probably better holding out hope for MapIt or whatever the homebrew mapping software is. After all, it already works, it's mostly tweaks and improvements at this point.
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