Use insulated tools and a steady hand to cut into the power cord and splice in the UPS. The UPS is configured to match phase with the power that's already in the cord.
Just discovered this now myself. The same company sells mouse jigglers.
Yes, it won't defend against cord cutting.
Edit: A more interesting defense I think would be to modify a surge protector for this specifically to defeat HotPlug. Only put your computer on a specific outlet and wire it so that if any other outlets complete circuit to kill power to the whole thing.
Definitely would go with my modified surge protector plan then.