Vegas does not do timecode and audio.
You can import Broadcast Wave Files (BWF) and Vegas will sync the start TC. Vegas will not record TC, will not render BWF and will not read LTC. You can use a LTC to MIDI TC reader box I believe but that means working in realtime and other complications.
All of that said I use an Edirol R4 to record four channels of audio along with 2 or more cameras to shoot concerts and have no real issues lining it all up by eye. For a 'film' shoot a slate and clapper is all you need to get the job done.
One solution that would help is to use audio kit that accepts word clock and something like a Big Ben. Then the clocks in the cameras and the audio sample clocks are all locked. You still have to line everything up manually but there's no risk of drift.