I say, absolutely. A live performance is a one-off experience (YouTube not withstanding) whereas a recording is something you hope people will listen to repeatedly. So I believe the approach should be to make the best recording possible. Lots of overdubbed parts means there's more for a listener to hear upon multiple listens.

And besides, there's lots of avenues as far as Christian radio and such, and if your recording sounds demo-ish, even if it is more honest, those doors will likely be closed.