A UPS will only consume power to charge its accu and to keep it fully charged, when a PC is connected to it and running, the UPS will not consume any more power, it'll only cause a bit more loss because due to internal resistance, the transport of electricity via the UPS is not 100% efficient, some energy will thus be 'wasted' in the form of warmth.
In short, no, if you power down the PC, the UPS will not consume more, or less power.