If the already have a recording of the song(which they should) then just play it from behind the camera with a stereo and tell them to sing and play their instruments with is. They should know it well enough to play along with their own recording.

I had played in a band some years ago and we did many music video shoots. Some of them were (relatively speaking) big budget stuff, paid for by the label (even overseas), but early on, many were self-financed.

We had a cheapo CD boom box that was sitting right next to the camera. We'd crank it up, hit 'Play' and sing/play along. Since the loudest noise we would make was from voices and occasionally, horns (electric guitars weren't plugged into anything), we could all easily hear the playback and sing/play along.

Editing this together is fairly simple. You put the CD soundtrack on an audio track in your NLE (FCP, Premiere, whatever), and start picking your video shots. You can align them by listening to the audio from the camera and lining it up with the audio from the CD so that there isn't any delay, flanging, phase shifting, etc.

As for the crew, you'll probably still need people to handle the light. Even if all is shot outdoors and God is providing the lighting, you'll need someone to hold bounce boards etc.

hey,
you should be able to easily sync, however keep the beats and measures of the song in mind, it could dictate the pacing in a way that you would end up actually shooting scenes based on them. when editing you will find that some scenes most have the correct action in order to develop with the song well. heres a video me and my wife did together, its pretty basic but it also shows you where you can go wrong. hope this helps,
cheers
http://www.youtube.com/watch?v=0x4KnRBt_lo