Just another quick point...

If you do this, and don't have a camera with line-ins, so you can record direct from your mixer, you might also record audio with a Zoom H2 type audio recorder, and fly that into the video editor to replace the camera sound. Nowadays, most of these digital devices keep exceptionally tight sync against each other, recorded 'wild' (no actual sync), at least for just a few minutes of a song, and a little 'slipping' can make up for any slight lost sync...

Things have improved enormously compared to the days where both audio AND video were all done on tape machines of one kind or another, subject to horrific drifting problems...