The sonic signature of your preamp is mostly the 6SN7 tubes. Voltage sag is not an issue (I think) because those tubes maybe draw 5mA each idle and maybe swing to 10mA on full signal. So the highest plate current is about 80mA for all 8 tubes which you do not hit unless playing full volume.
The 5AR4 drops the least amount of voltage for a given plate current than other standard issue rectifiers. At that plate current it's only about 5 volts, which should not really affect the linearity of the 6SN7 tubes. Rectifiers are more carefully chosen for power amplifiers, but in preamps I don't think will make much of a difference.