Hi!
unit
It's probably nothing to worry about. I had a PS/2 Model 80 whose power supply made a noticeable buzzing noise every time the power floor cleaner attachment was used on a household vacuum.
What you are probably hearing is the vibration of a transformer. I don't know specifically about the Back-UPS Pro models, but the Smart UPS and Back UPS RS models have voltage correction circuits built into them. These can adjust high or low line voltage without going to battery. Your unit could be doing this. If it is, you won't hear any beeping. The only sign of it is an entry in the PowerChute software--if you are using that and have a version that keeps an event log. (PowerChute Plus and the APC network management cards (only for the Smart-UPS) do have an event log. I don't know about PowerChute Personal or Business editions.)
I don't think you'll find that any damage is happening to the UPS or your computer. However, you really should try to ground the UPS somehow. For its internal surge protection to be effective, you may have to do so.
William