My answer would be, Yes, you do. There are 2 good reasons to leave the correct amount of head space in the jar when home canning.
1: Leaving the right head space is important to make sure you get a good vacuum seal. If you don't leave enough head space then your food can expand and bubble out with the air being forced out during processing. The food can get on the jar rim and prevent the jar from sealing.
2: If you leave too much head space then the food on top will very likely become discolored and again the jar may not seal properly because the processing time may not be long enough to force all of the air out of the jar.
So do yourself a favor and check that head space. After all, you have worked hard to prepare this food for your family, why let something that is so easily corrected possibly cause you to lose it.