From Cooper Bussmann on supercapacitors:
Supercapacitors are rated with a nominal recommended working
or applied voltage. The values provided are set for long life at
their maximum rated temperature. If the applied voltage exceeds
this recommended voltage, the result will be reduced lifetime. If
the voltage is excessive for a prolonged time period, gas generation
will occur inside the supercapacitor and may result in leakage
or rupture of the safety vent. Short-term overvoltage can
usually be tolerated by the supercapacitor.
Nominal means rated. Break the rules and behavior is undefined.
It does say overvoltage can be tolerated for a short time, but this does not imply using overvoltage in designs.
Extracted from Cooper Bussmann HB Supercapacitors data sheet:
Maximum working voltage 2.5 V
Surge voltage 2.8 V
Life (1000 hours @ +70 °C @ 2.5 Vdc)
Warnings Do not overvoltage, do not reverse polarity
Edit - acual part number posted in comments.
Data sheet for MAL222091003E3 (20F) clearly states the rated voltage at a case temperature of 65°C is 2.7V (peak current 25A), but if the case temperature increases to 85°C, the rated voltage is derated to 2.3V (peak current 20A). Measured at Tamb = 20 °C, P = 86 kPa to 106 kPa and RH = 45 % to 75 %.
The data sheet says:
Maximum operating voltage (refer to derating table) must not be exceeded.
To get the true application rated voltage, you will have to factor in ambient temperature, peak current, charge/discharge rates, cooling, case, moon phase, etc.
The supercapacitor does allow a surge voltage of 2.85V, but this is for less than 1s.
In Aluminum Capacitors, Vishay define surge voltage. I doubt it's meaning is different for supercapacitors.
Surge Voltage US
The surge voltage is defined as the maximum voltage which
may be applied to the capacitor for a short time
only .... The surge voltage may not be used for
periodic charge and discharge.
To answer the question, no, a supercapacitor rated at 2.7V should not be charged above 2.7V.
Will it work for your "non-standard application" (which I read as railgun), since you appear not to be concerned about useful life? A high rate of discharge will probably raise the case temperature to 85°C, which will affect the rated voltage, so I think probably not. This supercapacitor is not super-enough.