Yes you can use SD carts, though USB loader GX does not support it. Most of the others will support it though it might vary a bit depending upon what loader you end up using (I do like Neogamma, others will tell me to get with the times and go for something like wiiflow or configurable USB loader). For the most part you convert things to WBFS and stick that somewhere, though somewhere may be a defined directory for some loaders, on the SD card (maybe splitting if you are larger than 2 gigs) before loading accordingly.
Most would suggest that you just get another hard drive though and keep the SD for NAND, homebrew use, possibly some GC stuff, wiiware/VC and the like. However there are some very small Wii games (NSMB for instance) so play it how you will.