Theoretically it's possible, but in practice the lower input voltage makes it harder to convert it to +5/+12V. It becomes increasingly lossy and expensive - to convert 0.5V to 12V at 10W is not trivial to begin with. Voltage across a capacitor drops continuously while discharging (unlike a battery). So with a 2.5V capacitor, being able to use it between 1.25V and 2.5V is already pushing it. On average, discharge current at 10W is around 8A. The internal resistance of the capacitor (ESR) better be very low (it probably isn't) at this low voltage - even if it's 0.1 Ohm, at 8A we already lost 0.8V from out meager 2.5V, and now the useful energy is just 1.7-1.25 = 0.5C0.45V^2 = 5J, just enough for 500ms at 10W.