Yes, you can hook up a small tank to a full-sized grill, but the vaporization rate of LP inside the small tank might limit how hot the grill can get. 20 (4.3 gallon) tanks might not be enough to keep up with high BTU grills. Propane is a liquid fuel that must absorb heat from its surroundings to turn back into gas. Since it has a very low boiling point (around 40 degrees below zero), it will evaporate easily. For example, if there is a little space in the tank, then vaporization will happen more quickly, but if the space is big, then vaporization might take much longer to happen. If you use a tank that is too small, frost will start appearing on the outside of the tank. This means that it lacks the volume to provide for your needs, so you should consider buying a bigger one. Beyond that, which is a performance issue, I can't think of anything else negative since it's not really related to the LP.