I don’t think you’d have much of a problem with the recharging side. These small UPSes generally have very small charging stages, and they already take ages to recharge the battery, that is to say, it is already designed to charge for prolonged periods.
What it isn’t designed for is high power discharge over prolonged periods. But if you put only a small load on it, it will take longer before it overheats. So you can quite possibly get away with slightly larger batteries. How slightly… well probably no more than about four times the normal size. And I pretty much thumb-sucked that number.
Another thing to keep in mind: These UPSes often have absolutely attrocious no-load consumption values. They can sit there drawing as much power as the television they are holding up (eg, my Samsung 32" – I am a humble man when it comes to my television – uses about 35W).