the sd card isnt modified in anyway you just put files on it. you can still use it as you normally would you just need it in the wii when you want to play your emulators. the files that you put on the sd will show up in the wii browser which will give you the option to install a homebrew loader. the loader is installed on the wii itself and will stay there. it doesnt effect your online gaming either.
so to answer your original question. no. the only way to run anything is with the loader and the only way to install the loader is with the sd card