The world consumed more oil in 1939 than it did in 1929. A depression may cause consumption to decline a little, for a while, but it is not clear that it will cause consumption to decline faster than depletion. In addition, some of the oil that is being produced now is very expensive to produce. As prices go down, that production will come off line. A depression is also likely to increase political instability, further depressing production, if it does not lead to outright warfare.

Surely that indicates that to depress oil depletion then you would need a greater depression than the 30's, as supply and demand are going to be equal.
Counteracting that though somewhat is that AFAIK oil did not get more expensive in the 30's, and so there was less incentive to conserve.