I normally don't answer directly, waiting until some other comments arrive, but I'll make an exception to that "rule".
Dave is right, of course (Dave is
always right...
), but I can serve as witness: an XK, that holds 12 quarts (!) can pump oil when there is only 4 quarts in it. I used to drive one, and like Belatti's car it used to leak or burn oil. The fact is that I once ran it as low as 4 quarters, confident on coming back home to fill it with the oil I had in my garage. The problem: the last kilometer was a steep one: the gauge for oil pressure failed a couple of times. As I said, Dave is always right...
On the other hand, I imagine djones is talking about racing. You have to finish, but preferably first. The logic of a dry sump is not only the fact that it has a double stage pump, that it is easier to put an oil cooler and that (perhaps more important than anything) that you can install the engine closer to the ground and get a lower center of gravity: the fact is that the windage losses will be smaller. Normally you will find a "low half cylinder", close to the pump, that has a channel on it that collects the oil and distribute it to the length of the engine. This causes some losses. How much? I don't know, but that's what is needed to answer the question properly. If you take the risk to burn the engine, well, it's racing, not inheriting to your son the Volvo of your dad: in the second case, the answer is self evident. What a racer needs to know is how large is the gain and how large is the risk. Different models of cars (it comes to my mind the Porsche 911, with another 12 quarts!) will have different margins of safety.
Finally, on most pumps, at least in all the dry sump type I've seen, the oil is degassed, precisely to avoid the "bump-effect" Dave mentions.
