I don't think sending him a card does any harm. I can't imagine he'd be hurt or offended or bothered by it.
On the other hand, I don't think receiving condolences from strangers -- however well-meaning we are and however much we love Jake -- is going to make a huge difference in his outlook. He knows he has fans -- and knows, I'm sure, about the existence of BetterMost (and DC and imdb and ej, etc.). He knows his fans care about him, and care about Heath. I agree with those who've said the most valuable condolences come from people who either knew the deceased person, or who know you, the bereaved.
He's probably getting cards and letters and maybe flowers and gifts from people all over the world. They're probably being opened by an assistant. If we were to send something, I wouldn't be confident that he'd even personally see it.
In other words, I'd say anyone who would fee better sending him a card should do so. But I do think it's more about the sender feeling better than the recipient.