COMPUTER FAQ #10: IS IT O.K. TO DAISY-CHAIN SURGE PROTECTORS AND UPSs?
No. Each unit should be plugged into a properly grounded outlet for optimum power protection. “Daisy-chaining” protection devices (plugging one into another) will not provide any additional surge protection, or UPS runtime, and will effectively result in overloading the first UPS or surge protector on the line, knocking out all of the others downline. If you have them, connect each separately.