You could connect your battery string directly to the solar panel: the voltage is about right. However, your VRLA batteries are sealed, so you should never over-charge them.
Your "24V" panels probably have a peak power point around 36V, and an open circuit voltage around 48V. This is a suitable voltage range for running a "24V" power system, which actually runs at around 28V, charges at 30V, needs around 32V before losses, and needs some overhead so that it works in low-light conditions.
Running a "36V" system at about 42V, with charging around 44V, you wouldn't get very good solar efficiency out of your "24V" panel, and you wouldn't get peak charge current out of them, so they would not be 200W each (400W total) except perhaps under exceptional conditions when cold and new, running into a flat battery.
A normal charge controller can "handle" this situation, that is, it won't die, it will charge your battery, it won't overcharge your battery, it won't destroy the UPS. *Assuming the charge controller voltage levels can be configured for sealed batteries
The question is, can you "handle" the fact that you won't get 200W (each) out of your 200W (each) panels if you configure it that way?
Having said that, it's a UPS. You may never use it. You probably won't need 400W. And it's a stop-gap: your expectations don't have to be high.