I think a way to see the server details would be nice, but a hover wouldn't really work very well with the interface. I'll think about this one, though - it sounds useful.
If the person isn't in a server the Join/Play button just won't be on the menu.
I was imagining something like this (I took out the mouse :/)

Though, of course, you can do whatever you want. :D
I though of it cause it would be real useful to not have to ask the person what server they're on all the time. Also I like the second one much better because, as you said, you wont have to hover, although you could probably make that fade in and out when you put your mouse over or something.