Them sounding has very little to do with autotune. Vocals are not like guitar where you can simply buy tone. These pitch correction pedals for live use are chromatic so it is very different than studio autotune where you can change notes to whatever and create harmonies out of a single vocal track etc.
Trust me... if these guys didn't have autotune they'd still sound good.
About using autotune live... I have to admit that I've tried it and my only advice is that you still have to hear the uncorrected vocals or else you don't hear what pitch you're singing. And when you hear the off-pitch note and corrected note together it sounds terrible to you so it will not be an enjoyment in that sense. What I suggest you do is that you only hear your real singing and the pitch correction goes to FOH and hope that it's working.