Can I connect a surge protector to a UPS?

Yes, but your UPS may not be able to handle the load when your power goes out.

Sure, you can do this, but you would be better off with a line conditioner. Surge protectors often don’t react quickly enough to protect sensitive equipment, and do nothing about brownouts. A line conditioner does not have battery backup to provide power through a total blackout, but you can use one in between the outlet and the conditioner.