I know Dolphin can run some commercial games, but not perfectly. There are still some speed issues, which is why they say to use the best you can get. A low-end card may be able to handle it just fine. The problem is that Gamecube emulation as a whole is not entirely perfect yet. So I'm sure there are ways for GCN emus to run faster by fixing simple programming issues.
ps2 emulation is far from perfect, so it's not suprising the GC isn't emulated well, yet.
as for dolphin, the website says you need to be running xp 64bit or vista 64bit for the latest build. you're probably getting single digit fps because you're most likely running a 32bit OS. it's not worth upgrading the OS to get a emulator running, unless you dual boot.