Can a school suspend their students for simply having a Google Talk downloaded on their server even if they do not use it during school?

Yes, if that is school policy. It doesn't matter if they use it at school or not, if it is on a school server and the school doesn't want it there they can give a consequence to the person who put it there. The school will have some sort of internet usage policy. This is probably available to view. If there is a zero tolerance for any kind of downloading onto the school server then there is not much you can do to fight the suspension.