Not without putting safety at risk.
Should not be done.
And I also suggest that the plan be reconsidered.
A UPS is intended, for the most part to provide power to hosted devices when service power to your location is lost.
The UPS should be sized to provide just enough power and time to gracefully shut down the supported computer and its' monitor.
Plus UPS manufacturers do not recommend the use of surge protectors, power strips, and so forth with a UPS.
Most likely a general power outage will involve the loss of local internet service anyway making the router and switch moot.
Another issue could be that a ground loop would be created - ground loops can cause all sorts of problems.