I have read into vCenter and wondered
if there would be any benefit in using
it in such a small setup?
Yes, it is very helpful, even in small environments. One of the huge benefits you'll get by running you servers within VMware is that you're no longer tied to a specific piece of hardware. If your ESXi server croaks, you can easily move the files from the VMFS over to a new server and start them up without having to worry about changing drivers, incompatible HALs, etc.
Additionally, if you're like 99% of the businesses out there, your non-virtualized systems sit on hardware that is idle 99% of the time. By consolidating, you'll get better usage out of your hardware, possibly allowing you to decrease the number of physical systems needed.
Another benefit you'll get is the ability to create snapshots of your servers. This is very useful to do, say, before patching or other maintenance. If things to wrong, you can easily revert back to a known-good snapshot. Keep in mind that, for several reasons, it's not a good idea to keep large amounts of snapshots around for any one VM. So try and delete/consolidate snapshots when you've determined they're not needed any longer.
There are many other benefits and small conveniences you'll discover as time goes on. After getting used to operating in a virtualized environment, you'll find it pretty painful to go back to a non-virtualzed system.
To answer your other question directly:
Also, would it require a completely
dedicated server of its own?
If you have HA and have your VMFS volumes on shared storage, vCenter can run on one of the ESXi servers. If you are just using local disk and have no HA set up, then you'll want a separate server for vCenter.