Large-Gage needles, such as the ones used for donating blood or, evidently, what was suggested in the film, would indeed result in a rather significant mess if they were simply pulled out of the vein; the only reason they do not normally do so is because a gauze pad is immediately pressed onto the hole left behind. In my experience, this pad is pressed in place usually before the needle is even removed. Despite this precaution, I have seen small volumes of blood get squirted, usually no more than a few inches, while the needle is extracted and before the gauze is fully in place. I would not want to see what would happen without the gauze pad.
Gravity, or more accurately, positive head pressure, would help to move blood from one vessel into another one that is suspended below it. This trick is used in most normal whole blood donations, but is helped by the body's natural blood pressure.
On a theoretical side, a difference in blood pressures between Max and Nux could have aided the transferal, assuming that Max always had a higher BP. Some might even theorize that having Max in front of an accelerating vehicle would in a small way help to drive blood back to Nux through inertia. This should all be just chalked up to a little movie magic and impractical myth, however.