A larger cap (larger than the stock 0.1uF) can be used. It will not be without effect, of course - everything has an effect!
Offhand, that is without thinking about it extensively, I see only one possible source of problems. The coupling capacitor must be charged when the power supply starts, so there will be current through the grid resistor and hence a positive voltage on the grid of the 2A3. The stock capacitor plus grid resistor has a time constant of 25mSec. With 2.2uF for example, that time would be 550mSec. This is long enough that the 2A3 cathode filament will be heated, and a positive grid voltage during this startup transient can cause excess current to flow before the filament is fully warmed up. There is a danger of stripping the cathode, rendering the tube worthless. This can happen very quickly, or be spread out over time, depending on the tube, the power supply time constants, and probably other variables that have not crossed my mind yet.
Sonically, there may be other effects even if the tube is not badly affected. The 25mSec time constant gives a bass rolloff at 6.4Hz, down 1dB at 13Hz - and more important, down 21dB at 0.55Hz, the lowest warp frequency for 33RPM phonograph records. That's just the first example that occurs to me. The output transformer/plate choke/parafeed cap won't pass those low frequencies, but excess level at low frequencies could overload the 2A3.
There may of course be a sonic benefit - much stranger things have happened! If you have some tubes you don't mind risking, you can try it and see if you hear anything that you like. If there are big enough benefits to your ears, then there are ways to address the cathode stripping problem.
