Relying on 'hanging a big old cap' on the output of a voltage regulator is most likely not going to fix the 'problem' and likely to interject new problems. Perhaps if you could supply the following data, then there is a chance, using some math to actually determine if a properly sized cap is pratical or useful or not.
Actual current max 'burst' amount.
The duration and period of the 'bursts'.
Your voltage sources max current capacity and output impedance.
Capacitance value and ESR value of the cap proposed to use.
It's always preferred to size the voltage source to handle the maximum current demands in the first place. 'Hanging caps' is the shade tree mechanic version of electrical engineering.