Your amp will have a substantial (probably not substantial enough, but I digress) capacitor bank already as part of its power supply. Adding additional capacitance to this is unlikely to solve your problem, and there are resonance issues that can arise from the resulting second order CRC circuit.
However, this is not a subjective case - you have a testable symptom. With that in mind, I suggest you try to borrow a capacitor, and then you can test for yourself if it resolves your issue. To gain a benefit from the capacitor, it should be as close as possible to the amplifier as possible - practically across the power terminals.
My bet is that you won't find it fixes your problem, particularly not the current surging (a cap charges much faster than an amp draws current). But since you CAN test it, please do.