Yes. As long as the game ID (e.g., ULUS-10006) matches between both players, compressed vs. full ISO works fine in LAN mode.
Once you have found your compressed file, here is how to run it: midnight club psp highly compressed
For Android (PPSSPP Emulator):
For PC (PPSSPP):
For Real PSP Hardware:
There are three primary Midnight Club titles for the PSP. Here is which ones you will find in compressed formats: For PC (PPSSPP):