FileMaker Server will speed up everything about accessing your database over a LAN or a WAN, including the speed of sorting records. However, sorting is always done on the client side.
FileMaker Server also includes dozens of other critical features such as automatic backups, performing scripts on the server, SSL security, and more.
What Scott says is generally true about FileMaker that sorts are done at the client side. There are some exceptions such as if you're in WebDirect, then it is all processed on the server side. Also, you can use PSoS to build an array on the server and return that value already sorted. Then you have to figure out how to display it such as with a virtual array. FileMaker has always been painful slow at sorting and is a real achilles heel in performance.
You will get the best FileMaker performance by copying those databases from the across the LAN to your hard drive and opening it locally. But opening FileMaker across the LAN will result in poor performance. If you need to work across the LAN (or WAN), then FileMaker server is designed to make the process more efficient. Plus there are many other benefits to FileMaker server from backups to schedule scripts to security to multi-user support to WebDirect, etc.