About the only thing the SuperCaps would be great for is helping with surges, both before and after the inverters. Having that extra "umph!" available can help lessen the hard hitting draw that some devices require during startup (examples would be heavy duty induction motors like washers, vacuums, or even ceiling fans if they are all on when the main switch it thrown, air compressors/conditioners, fridges, etc)
It isn't unheard of for an induction motor to pull 2 - 3 times their rated amperage for up to 2 seconds on startup