Yes but they must be burnished or roughed up somehow for the paint to stick and not peel off. Don't know specifically about faucets but will probably be the same.

OP has been up awhile and not much response. I would suggest experimenting with automobile paint. Buy, beg or salvage a few old doorknobs and experiment first as automobile paint is not easy to work with. At least I found I did not like my first few efforts.

they make quite a few different primers for different surfaces, ex: wallpaper,porceline tile,
check hardware or paint supply stores

I think WalMart carries paint especially for metals.

Suzi