The short answer, I think, is no. Even a small sump pump pulls something like 6 amps (720 watts) so you'd need a pretty large UPS to keep on running for any period of time. From APC's runtime chart a 1500 VA back-up (retail $250) would keep 700 amps running for 5 minutes. Motors have a fairly large in-rush of current on start-up too. I don't know if a UPS is designed to handle that. The pumps sold with battery back-up systems are 12 volts DC, so you couldn't just plug one into a UPS either. It is probably far more cost effective just to buy a automated battery backup sump pump system.

Many back-up sump pump users and installers have switched to water powered pumps Such as one by Zoeller & Liberty (Liberty SJ10 is one I like best) No expensive batteries to buy and maintain and water powered units run forever without needing a charge. You will find that the water used is less than charging battery. Safer also as no fumes or fire hazards associated with having a battery in basement. Remember, you need water to run so best used with municipal water supplies. (no wells) Here is a link that might be useful: Liberty SJ10

I think a backup pump with it's own piping and wiring is a good idea. My neighbor was recently away...the pump came on, but the hose from the pump developed a tear....water all over...had to tear out the walls in finished basement, etc.. A backup pump with it's own piping would have saved her. I've heard of pumps with battery back-up and it makes sense. I really don't know any good brands. The thing that bothers me from what you are describing is..."a back-up pump outside the pit." I don't know what you cellar is like, but it sounds like the water would have to rise about 5"-6" before the pump would kick on. That is the reason for having a pit...the water drains into the pit and is pumped out before there is any accumulation of water on the floor. I'm assuming you have a full basement??

It sounds like you answered your own question: you have a sump that needs almost constant pumping, so you definitely should get the most reliable system you can afford. You won't go wrong with a Home-Guard. They are essentially bullet proof, and will pump forever. I have no experience with Baseguard, but if it is sized right (i.e., has the ability to pump the maximum amount you will ever need) it will probably work fine, as these types of pumps have no moving parts and are generally very reliable. And, as you have painfully learned, when a pump runs as much as your's, you need to check on it and clean it out at least monthly, if not weekly.