If the leaves have completely died, there's a good chance that the garlic cloves will have no covering, with the cloves exposed. You can still use them, but they will not have much of a shelf life.

if the plants are dead you should harvest. the bulbs are going to rot if its wet.

Ditto. Not only is there a chance of spoilage, if you have heavy rains the cloves might sprout... and the closer you get to Autumn, the more likely that sprouting will occur.