Just make sure that the ups unit can handle the amp draw of your server setup, including anything that gets powered along with it. You can use whatever size of battery you want as long as it is 12 volts, but capacity of the ups relative to load is critical. If more amps than designed are pulled from the ups, it will either quit if it has that emergency shut down, or the overload could kill it.
I recycled mine when I discovered that my new desktop setup would overload it. Had that not been the case, I would have re-powered it with a larger external battery exactly as you suggest.