You'll be better off with a 4 channel recorder where you can capture the tracks discreetly. 4 mic mixes, depending on microphone placement, are prone to phasing issues/comb filter effects when mixed-on-the-fly. Similarly with SBD + mic matrix recordings, unless your mics are either on stage or within 20-25' of the PA/stage, you'll have too much delay between the feeds to mix on the fly.
It is better, and you have more control, doing post-mixes of anything more than 2 channels IMO...the only exception being 3 channel mic mixes like shotgun x2 + card/omni recordings.