Running everything through Live plus recording, is gonna require a noticeable latency especially for vocals. When you play an instrument through Live it's less noticeable than singing into Live and hearing to the speakers.
I would try using Live for 'some' processing, i.e, reverbs and such, but I would also try setting up some kind of zero latency direct monitoring.
If you were just talking about a few mic's and instruments, maybe not such a big deal.
Nevertheless I would try it. If the band is not "dependant" on monitoring the latency might not be a bother. For example, if everyone is confident singers, there's plenty of volume on stage, no real need to "hear" the mix on stage, then I would say your idea will work fairly well.
The computer and soundcard will make a difference, and there is only one way to find out if they are capable.
Well the band will have in ear monitors and the singers have wedges. I would say we need monitoring.
Also I don't expect all instruments to need effects. I expect
Drums-compression and eq and filters and reverb.
Vocal - reverb with eq
Guitar - Nothing
acoustic - Nothing
Keys - Maybe reverb
Bass - nothing
Would zero latency direct monitoring be done with effects per track?