You can have them do a test and adjust the system depending on the filter that's installed to make sure it's moving enough air (though that is mainly important when heating to prevent the heating element from overheating).
It is also important in the cooling cycle for two reasons.
1. If there is not enough air moving over the air-conditioner coils there is the possibility that they will ice over. This has a cascading effect where there is less transfer through the coils and more ice builds up until the whole thing is a block of ice. This most often happens though when people buy condensers that are too big for their system (the thinking being the bigger the better the more cooling, but it is a balance within some tolerance) but can also be done on the other side by reducing airflow too much.
2. Less airflow can also mean too much condensation in the air which can end up sitting in the ductwork and causing it to rust out. This happened to my parents when they installed extra filters in their HVAC system. I guess this is similar cause as #1, just different potential effects.
