You probably won't have any problems when you're running a server on it. It's still good to let the battery drain every once in a while, so just be sure to reconnect the power in time if downtime is a problem.
If its just to mess around with/ learn on, they are plenty powerful enough to be a server. I was running an iBook as a file server, and while it didn't work out in the end, the machine had plenty of power for the job- and that was a G4.
Sounds like running a server 24/7 should be ok. How about running it 24/7 at 100% doing folding@home?cIt seems like it's ok, but the fans are running at max all the time.