The fundemental problem of trying to use 'super caps' to power ucontroller ships is that a cap's terminal voltage drops in a linear manner determined by the R/C time constant where the micro's current draw represents the R. This unlike batteries that maintain a nominal constant terminal voltage through out it's capacity rating (either expressed in AH or mAH). Micros usually require a regulated constant voltage, even if they have a wide range of voltage they can work with, but a constantly decreasing Vcc that varies with current draw would make for a pretty fragile environment in my opinion. I could only see a 'super cap' possible being useful as a 'stay alive' circuit if one put the micro in some kind of deep sleep condition and needed to remove the normal Vcc voltage source. If the super cap was diode isolated from the main voltage source it could continue to keep the micro in sleep mode thus saying state of SRAM and control registers for some period of time until the normal Vcc could be replaced?
So my bottom line opinion for the OP's question is NO, except for possibly some exotic short term 'back-up' mode.