No, it should be fine. The problem is with high draw devices that can spike their power usage when they are warming up or running. Older laser printers and multi-function laser or thermal printers were real trouble with this. For new printers, the inkjet combination ones work fine.
As long as your UPS will not exceed its recommend power draw, you should be set. The scanner part may not draw a constant amount of power, so it is better to use an AVR (automatic voltage regulation) or higher end UPS with it.
If you want an authoritative answer, just call up HP support (their USA number is 800 474-6836 ) and ask them.