The distro (Fedora) has nothing to do with the partiton sizes. Any distro can have partitions of any size.
I would rather expect most servers to have a small root partiton, as for the most part, nothing should go in root. The key is, what partitons are there, and what size are they? If you have a seperate /var, /usr, /etc, /home, and /boot, and they are all of decent size, then you're all set. The size of the disks aren't a huge factor in any case. Unless it is a file server of some sort, most web servers would be just fine with under 10GB of total size. It all depends on what the server is doing, and to how many people, etc....