The only time I don't sing with just a banjo is when I'm playing a banjo tune that has no words (that I am aware of). I never cared for Pete Seeger's banjo playing as much as his half-brother Mike's. Mike Seeger's Southern Banjo Sounds is an incredible collection of singing with banjo, singing with numerous and somewhat unusual banjos and performance of music not often heard. All banjo oriented of course. 26 songs played on 24 different banjos (or something like that).
Peggy Seeger is very good. But give a listen to Gail Fratar or if you're lucky enough to be near Augusta, Missouri or can acquire a cd produced by the Augusta Bottoms Consort, listen to the playing and singing of Gloria Bauermeister. I agree that Debbie McClatchy is more than worth listening to as well.
To be honest, it never occured to me that someone might wonder if playing a banjo and singing along with it was something do-able.