Hi Rob, welcome to ETO!
No, the mineral oil will not improve the performance of standard ceramic capacitors.
The concern about capacitors used in Tesla coils is the dissipation factor (The ratio of the ESR over the reactance of the capacitor). Higher dissipation factors can cause the circuit to operate inefficiently, leading to heating from the inside out. This won't be helped much (if at all) by mineral oil.
You really need some MKP or MMKP capacitors (metalized polypropylene). These tend to have much lower dissipation factors and are ideal for Tesla coil applications. The dissipation factor should be less than 0.001 in order for a given capacitor to work well in a Tesla coil primary tank circuit.