No one really knows, and the answer depends on how the industry manages the downtime.

But in principle sure: storage filling up means that production needs to be halted because there's nowhere to put the oil. Production being halted means that facilities are going to be shut down, workers laid off or furloughed, and equipment mothballed. Some of those processes, as with all industry, are going to be expensive to start back up.

So if the industry doesn't (or can't, if it actually runs out of liquidity) have the agility to get things moving fast enough during the recovery, we might see a price shock in the other direction.

Or we might not. Certainly no one here is going to be expert enough to make a good prediction. But the principle is sound.