I have a sump pump that I would like to put a battery backup on. All the backup systems I've seen look like they require a secondary pump. I can understand why you would have the secondary pump on the battery with the primary plugged in but can I just plug a single pump directly into a battery with the battery plugged in? Is this incorrect to do?

A pump "plugged into a battery" has very limited backup protection. It is actually plugged into an inverter that will make AC power for the pump. The problem is that the power inversion process only provides VERY limited running time AND if the pump had some sort of failure, you are out of luck. Instead, I would recommend investing in the NEW, nearly FAILPROOF PeakFlow Pumps 5600 ePump. Notification of alerts via PHONE and EMAIL. Self testing, self diagnosing, dual pumps, dual sensors. If ANYTHING ever fails, you will know about it...BEFORE there is a problem. UNBELIEVABLE! 5 year warranty!