Does Garage Band support recording with video??
No, GarageBand does not record video, only audio.
You could use iPad's Camera app to record video and GarageBand running in the background to record the audio. But that would require BarageBand 1.3 on IOS 6.0.
Which version of IOS and GaragBand do you have?
Also, to use the iPad Camera with GarageBand in the Background you would not be able to play the touch instruments while jamming along - you would need to play loops and smart instruments.
To record audio in GarageBand in the background open the settings (in Instruments view, press the wrench) and enable "Run in Background".
Then GarageBand will continue playing or recording (with the built in microphone) while you record video with another app.
Regards
Léonie