Hey there... I live in PA too and where I am, losing power is common and so is my basement flooding. My basement is only 10x10 but it houses my furnace, water heater, and well water pressure tank. This is no lie... I take on water all year long... the basement is stacked stone, below ground level, and I have a huge hill right behind my house, literally 4 feet from my house. All water constantly runs into the basement. We lost power during Irene and I was taking on 10-12 inches of water every 2 hours!
So, with all that said, here is what I have learned over the years. I started with a single pump and that was fine until the pump went bad one day and I didn't know it. The basement got 4 feet of water before I knew there was a problem. I got a second back up pump in case the first one failed. That worked but then we lost power one day during a heavy storm. Took on so much water, I could have dived into it. Got a generator to run the pumps but as a side bonus, it will also run the refrigerator as well. The only thing I needed was some way to know if I was taking on water to a dangerous point in case anything failed. Well, I found that too. Home Depot sells a battery operated water alarm.
For your situation, I think all you're talking about needing is a way to keep your pump running. An inverter won't do that but they do make a battery operated back up sump pump. I have heard it's a life saver, though it is costly. On the other hand, it's worth spending the money to keep from ruining things in the basement.
Basement Watchdog Battery Operated Sump
Here is the water level alarm I mentioned. It's worth the money simply for peace of mind.
Water Level Alarm
Hope I was able to help you out.