Frequently Asked Question
Typical power strip is rated to 3000-4000VA, while a small home UPS could be 650-2200VA. If you connect power strip on the output of the UPS they are not connected adhering to a cascade rule, where limitation grows as you increase distance from the load. This is especially important for power strips with fuses or breakers or equipped with surge protection. This essentially means that power strip (surge protection) would never react to overcurrent, as the UPS would be first impacted.
Additionally, in case of surge protection, it is recommended to connect it before the UPS (as seen from the perspective of power network). You have no benefit in protecting your surge protection from power cuts, but you can save your UPS if you protect it from surges.
Nevertheless, it would function, so there is no serious danger considered.