This is something I've been thinking about a lot. Hamilton is my favourite show, and it would definitely ruin some moments to know they are not authentic vocals. But at the same time, I've heard enough variation in a bunch of performances to feel like the end of One Last Time, the ending of Room Where It Happens, ect are real. And overall there aren't as many moments like Christine's crazy top notes or the ending to Thank Goodness in Wicked - the hardest part is often the rapping, and I can't see how they'd prerecord that. And there is some flexibility whether actors want to go for the higher riff in Satisfied, what they do with the end of One Last Time, ect.
But yes they do use amplification, some prerecorded sounds, and at least one prerecorded voice (the really low voice that says "DAMN" and a few other things - it's actually LMM's voice distorted and lower)
OH and the 'rewind' on Satisfied is recorded, obviously, as you can hear Angelica's voice when the actress is standing there and obviously not singing. One thing I did notice and appreciate is the rewind is recorded again with act actress so it's always in her voice. Some of the music is prerecorded as well I think, just to round out the orchestra.
Maybe I'm naive but I feel like Hamilton, while using synthetic elements, are pretty honest about using it to enhance the performance separately from the actors talent if that makes sense. Not covering for what actors can't do but using it in different ways to put on a cool show (Such as the DAMN voice)