homebrew, yes.
wii system menu, no.
anything over 4gb *and most 4gb cards for that matter* are sdhc cards.
edit: re-read your question and not just the topic. yes you can use a standard 4gb card (non-sdhc) but you must have over 2gb filled on the card. (music, pictures, video, whatever) it has been known to cause corruption over time, so imo, your better off just using a 2gb or smaller card for wii system menu uses.