Plugging a surge protector into a UPS battery backup
A UPS provides the surge protection on the input side of the circuit so plugging a UPS into a surge protector is the same as daisy chaining surge protectors. Due to the potential for harmonics and feed back into each others surge protection circuits one or both could blow up causing a fireworks show and or a fire.
The output of a UPS is usually a square wave and not a sine wave. Surge protector circuits are designed for a sine wave input. Unless the surge protector is designed for a square wave and even then I would take it with a grain of salt.
best bet = don't ever do it.
How to annoy a liberal: Work Hard and be Happy. In the words of John Smith who saved the Jamestown settlement: Those that don't work; will not eat. We need to learn from history.