yes, you can play retail Gamecube disc with DIOS MIOS installed, and even use some DM settings if launch from a loader instead of the Wii's Disc channel. (video mode, language, debug, etc.)
The only issue you can have is that you need an USB drive connected, because DIOS MIOS starts by initializing the USB drive before checking the inserted disc, if there's no FAT32 USB detected your disc won't launch.
If you prefer, or if you have difficulties with USB init, you can install DIOS MIOS Lite instead. It will then check the SD card instead of USB at launch.