Absolutely not. The PSP and Wii are fundamentally incompatible architectures.
| Aspect | PSP | Wii |
|---|---|---|
| CPU | MIPS R4000 (Allegrex) @ 333 MHz | PowerPC (Broadway) @ 729 MHz |
| Media | UMD (1.8 GB optical disc) | 12 cm DVD (4.7/8.5 GB) |
| OS | Proprietary PSP OS | Wii System Menu (IOS) |
| GPU | Custom 3D + 2D engines | ATI “Hollywood” |
The Wii cannot physically read a UMD, nor execute MIPS instructions. There is no emulator for PSP on Wii (the Wii lacks the horsepower for playable PSP emulation).
To play PSP games: Use a PSP, PS Vita, or PC/Android via PPSSPP (excellent emulator).