As for storing for a few months, fuel mix you make yourself is suggested be used withing a couple months, but commercial pre-mix actually has a unopened shelf-life of 5+ years and an after-opened shelf-life of 2 years.
The reasonng to the reduced shelf-life is due to oxidation of the fuel. When getting from the pump yourself, the gas has been passed around several times just to get to your tank (refinery to trucks to station to your can). Each time it gains oxidation, and every container along the way has space for air. Sealed commercial pre-mix minimizes all that. It also is ethanol-free and has longevity stabelizers.
I don't know of any tests, but it could be a reasonable assumption that prior to storing your saws for a few months (though maybe not if for years) that to fully top off your fuel tank, preferrably with commercial pre-mix, would reduce the oxidation within the saw's tank since there is little or no air inside. Though if you have gas still in a mostly empty can (particularly home-made mix), then you can expect it to deteriorate and probably should toss it.