I initially thought it would be overkill to have the birthdays on the banner, but if they're in smallish print and just acknowledged as "Today's birthdays" or something simple like that at the bottom of the banner, I think it's harmless and lends a kind of family feel to the index page.
Anyone who doesn't wish to be acknowledged can leave the birthday line blank in their Profile. The birthdays shouldn't be hard to track, since the software automatically puts them onto the calendar, right? It shouldn't matter whether the poster is active or not. If they provide their birthdate, then they get listed. (I agree that it would be good to mention that it will go on the calendar if they list it.)
In regard to what Katherine brought up, I think it's nice when friends spontaneously start birthday threads for each other. Sometimes it's a tough call on whether a poster is known by enough people to get a nice response, but if someone feels the urge to acknowledge that person's birthday, then that's the best indication. I don't imagine that folks who post only rarely would be expecting their own thread and feel hurt if they didn't get one.