The oil quenching would probably be from the solution treatment temperature, not the aging temperature.
With very large sections, there may be concern that air cooling from the solution treatment temperatures may not be rapid enough to prevent transformaton. I am not sure how large the section has to be for this concern to be valid, however. I know that air cooling is fine for solids up to 6 inch (150mm). I think it is more important that to cool it below 100 deg F.
I cannot remember the specifics, but I do seem to remember some specifications in the mid 1980's that called for air cooling or oil quenching from the solution treatment temperatures for 17-4.