Yes, it does. In fact, the impact of tank size on an air compressor is immense.
The bigger the capacity of the tank is, the better it works. So, do buy the biggest tank you can afford so when the compressor is filled up and stopped, you’d have a larger reservoir of compressed air ready to use.
Nonetheless, if you only need a unit to help you change the tires of your car every once in a while, a smaller tank size is acceptable.