Modern-day UPS systems have "intelligent rectifiers" which ensure that the current taken from the input source is both in phase with the input voltage, and relatively sinusoidal. This is all done regardless of the load presented to the UPS, be it hi-tech, inductive, or resistive.
But lets take the inductive part. The main issue is that the current lags the voltage. In order for the power (watts) to be transferred, the current (i.e. VA) needs to go up. When the current goes up, the losses between the source and load (e.g. motor) also increase because of this raised current. Ok, so far we haven't said anything new. But let's consider the UPS for a moment.
The output of the UPS is a transformer (of some nature). Feeding this is usually a huge bank of IGBTs switched in time with the incoming supply (as part of the 'keep things efficient' scheme). Feeding this is usually a whole set of batteries. Feeding this is the intelligent charger spoken of a moment ago. Again, nothing new revealed here.
Now consider the lagging current curve. First of all it is not in time with the voltage. Even if the UPS controller was designed to sync the output current curve to the input voltage curve as part of the PF correction, this is sent way out of whack when the inductive load is switched off, and the UPS is left having to re-synchronize, but it has to do this slowly so as not to disturb other loads.
Even if synchronisation is not considered, the current required on the output is higher. This means higher losses on the output transformer, purely because of impedances within it. The IGBTs have to work that much harder to produce the current curve, and will therefore have higher heat output. The battery system will have to provide power during the current peaks, and be recharged during the phase crossings. This leads to battery gas output and dielectric loss.
With the UPS having a higher heat output means its cooling system has to work harder because, if it didn't, the electronic components would suffer premature failure (which means you lose the 'protection' of the UPS).
Before we end, cast a quick thought to the cooling system we've just spoken about; If it were the inductive load, consider how much the cooling system was actually cooling itself before it cooled anything else.
Rather a compelling argument, don't you think, that although a UPS may hide the fact there is a power factor problem on its load (because its own input is near resistive) does not mean the UPS has performed power factor correction and therefore reduced losses. If anything, it has increased them!
"There has been a sudden increase in power factor correction capacitors....."
... so where's my cut!?