An offline UPS will switch to battery if it doesn't like the input. What qualifies as acceptable input depends on the design and specifications of the UPS. If it expects a real grid-like sine wave and doesn't see one it will reject it, regardless if the load would like it or not.
> If it expects a real grid-like sine wave and doesn't see one it will reject it, regardless if the load would like it or not.
But why would it require grid-like sine wave and not go along with whatever is the source, provided source can still be used to charge its batteries? I saw no answers yet, and this "why" is the very key to the discussion.
For example, a common topology in offline UPS is that the inverter and the charger are the same circuit driven differently[0] - so you can't charge the battery while the inverter is carrying load. This is popular at the low-end because you have literally half as much UPS, but makes what you're describing impossible.
Another common issue at the low end is that the inverter isn't thermally sized to run non-stop, they know they can cut a corner because your battery presents a finite and known duty cycle.
There are ways around this, but at some point you end up fixing the wrong problem - eg, it's cheaper, safer, and more resilient to buy a transfer switch instead of uprating two UPS to be capable of daisy-chaining.
It's not sarcasm. When nobody tells you a why item and you think that's because literally everyone else is dumber than you, it's likely there are odd numbers of sign errors in your heuristics.