From what I could find it is not possible. The displayAsPassword functionality is actually defined in the flash.text.TextField class, but I couldn't find any accessible way to change the password character. Sorry, I tried.
I don't think there is a way either. If you're really desperate, you could try overlaying another TextField on top that has bullets for the characters underneath
Flex SDK Developer
Adobe Systems Inc.
Thanks for all the responses. I was thinking of a solution like the one above, but I didn't know if there was a "cleaner" way.
Just use a font that has a different SHIFT-8 character for the * (asterisk).
Webdings, for example, has an envelope icon for the SHIFT-8 character. Set your password TextField to use it and you'll see your password shows envelopes instead of asterisks.
Find or create a font with bullets (or anything, really) for the SHIFT-8 character and you're set.