How an audience reacts to a gig is quite a genre specific thing, I think anyway.
What we're talking about is performance. There's an excellent book called 'Musicking' by Christopher Small. He defines 'musicking' as: To music is to take part, in any capacity, in a musical performance, whether by performing, by listening, by rehearsing or practicing, by providing material for performance (what is called composing), or by dancing.
So either by going along to watch a gig, or by being a musician performing, we're all taking part in the process of 'musicking'. The book is really excellent, I encourage anyone who has any interest in music to read it, particularly if you do perform.
There's another article that I was reading recently called 'Performing Performance: Interface design, liveness, and listener orientation', by Mark J. Butler. It's aimed mostly at the electronic music scene, but is sill relevant.
Performance is central to what I do, and I guess to what we all on here who gig do. I'm personally very aware when I gig that people are watching me. Even though it's only me sat on stage with a MacBook and a bunch of effects pedals, I do make a definite effort to interact with the music, and to demonstrate my part in what they're hearing. I definitely don't dance or move about, but that's not expected. It would be expected though maybe in a rock and roll gig, and definitely would be in a more dance orientated genre. Which is my point.
The article by Mark Butler describes how electronic musicians, and DJs sometimes over state their movements on stage, there might only be them on stage with a MacBook and nothing else, but they are still 'performing', and by the somewhat dramatic gestures they're showing their participation in the production of the music.
I occasionally play gigs where I'm sharing the bill with laptop artists, sometimes they're using treated instruments too. Again, they're engrossed in what they're doing and their interaction is evident. They're not expected to get up and move or dance, but it's still obvious by what they do do, that they're not just checking their emails :).
To reiterate, it all depends on the actual music that's being performed.