I think it might, especially if you are running Lion or Mountain Lion.
My son set up a Minecraft sever on an old mini I was using as a HTPC. It worked fine (on Snow Leopard) for weeks, but then I upgraded to Lion.
The machine ran slower and slower until it became unusable. Then the hard drive crapped out and Lion would not even boot. I wiped the hard disk, checked for errors (disk utility said it was fine) and reinstalled Lion. The mini ran great for a few weeks and then the same thing happened: ran slower and slower and then would not boot. I assumed the hard drive was bad since it was old (a core duo that I had upgraded to a core 2 duo.)
I bought a new mini (refurbished) from the apple store. This one had the newer unibody design. It also became sluggish very quickly and then wouldn't boot. (This one started with Lion but had been upgraded to Mountain Lion.)
When it wouldn't boot, I tried to launch from the recovery partition. That was also corrupt. I finally was able to reload Mountain Lion, stopped the Minecraft server and have not had a single problem since. That was about 2 months ago.
The problem may not be the Mindcraft server specifically, it may have been the way my son had set up the scripts to run it, I don't know.
What I believe was happening is this: In Snow Leopard there weren't any problems because the mini was set to reboot every night. With Lion and Mountain Lion, the machine rebooted, but then it reloaded all of the programs as they were before the reboot. I think there were multiple instances of Minecraft running.
I also think that Minecraft over-wrote parts of the disk, eventually over-writing the OS and even the recovery partition.
Everyone is much happier now that the Minecraft server isn't running on our little mini.
PS I said that the fault may have been with the way my son set up the script to run Minecraft, and it may. However, he should know what he is doing, he is in his senor year studying computer science engineering at a Big 10 school.
