There are several potential issues with not using a ground for your UPS or workstation. Most notably is the risk of operator injury. For instance, in the UK, if your appliance (UPS, PC, handheld drill) is not double insulated (identified by having 2 boxes, one inside the other and an almost complete plastic covering shell) it must, by law, be grounded. This is to prevent a short inside the unit from making the outer shell "live", in this instance, if an operator were to pick it up, they would act as the conductor to ground. However, if there was a grounding wire in place, the copper/aluminum/other should be a much better conductor than a human body in most cases and will harmlessly discharge the current to ground, usually tripping a circuit breaker or blowing a fuse.
The other reason is for electrical noise, a non-grounded appliance can introduce a 50/60Hz hum or other interference into the devices that it is plugged into, or in some cases, near.
A true ground is actually remarkably easy to obtain, it is "simply" a matter of driving a (usually) copper spike into the earth and having this connected to your electrical system and any exposed metal fixings (copper pipes for radiators, water pipes for taps etc). In the UK it must be easily inspected but a total cost for the parts required (earthing rod, couplers and inspection pit) is well under £50 or 3500 Peso.
To answer your question succinctly, no, it should not harm your UPS not having a ground but it could potentially harm you. It may also introduce "peculiar" networking errors, especially if your are fully utilising a gigabit ethernet connection, i.e. running iSCSI to multiple machines etc.