it depends where they are stored, IIRC gamecube save data (using a virtual memory card function) is stored where the games are stored..
if your games are in a usb drive, the save data goes to a folder inside the usb drive
if you have your gamecube games in the sd card, they are saved to the sd card
as long as you copy the save folder, you will not loose progress
another option (which i did) is buying a real gamecube memory card and don't use virtual memory card functions.. this way you can use the card in a real gamecube and it's a memory dedicated for the gamecube saves
PS: be right back, i will check where they are saved on my wii and tell you)
edit: i was right, the saves will go to the same place where you got your games saved.
if you launch a game through usb, it will be saved in the usb drive
if you launch a game through the sd card, it will be saved in the sd card
https://gbatemp.net/threads/nintendont.349258/#NintendontSavegames