Hi, I'm pretty sure your UPS would condition the output voltage (see specifications). However, I've noticed that your UPS is of type "interactive" i.e. you get power normally from the mains unless you experience a power failure in which case you then get it from the battery. I assume that the conditioning of the voltage that the UPS does is when it powers your equipment from both the mains and, definitely, from the battery. Why don't you email the manufacturers of your UPS asking them if the UPS includes a conditioner and whether it is a good idea to include an extra one or not? If it is beneficial to use a conditioner then I suspect it would be better to put it before the UPS.
It says its output is a sign wave and its surge suppressed, which means you do not need the conditioner. The sine wave from the UPS will likely be very clean, far cleaner than the PSU is designed for, PSUs are designed to take in some fairly dirty power without having an issue.