No, the only save that is in the battery backked memory is from the last thing you ran. When you next use the cart it will be written to your SD. If your battery dies before you play w/ it again, yes, THAT save would be lost. If the game in question had an older save on the SD, though, that would still be there.
Don't worry too much about the battery, as long as you use your EZ Cart even semi frequently it's unlikely to run dry.