If you like modern musicals, and/or the hip hop of the 80s and 90s, you are almost guaranteed to enjoy Hamilton, even if you aren't already familiar. Personally I was glad to know the music well, because I could focus my attention on the presentation rather than needing to figure out the plot (Hamilton is sung through, like Rent, so the entirety of the story is told through the music). Then again, who knows -- I might have been even more transported if I'd experienced the whole thing at once as a performance, rather than as just the music.

I can't speak to the experience of watching it cold as compared to having listened to the soundtrack just once or twice. I'm having dinner tonight with a couple, one member of which did it each way, so I can ask and see what they think. :)