Is it bad for you if you put Sharpie on your fingernails?

No, Well if I were you then I wouldn't do that because:

Sharpies are permanent markers and it isn't nail polish so it won't work on nail polish remover I think! But I wouldn't take a risk. But I am not you so go ahead and try it if you want to... If you will then I recommended you to put a dot on your nails with a sharpie instead of the whole nail.