Originally Posted by Plankton

You, or the engineer I guess in this case, will have better control over the final mix if you record everything separately. You can play live and still get separation through a multi-input interface, but it all boils down to what gear you have access to. Having everything all recorded into one blob of a track limits a lot of post editing capabilities and is usually a bad idea in most cases, but sometimes people pull it off to an extent and get that 'live feel' with a good balance in DB separations, but mostly it just comes out muddy and everything competes for space in the mix. Put in a little more work than just a one-off performance and you'll likely get better results.