Last year I purchased a 50-year-old home. Central air and heating were installed about 12 to 15 years ago, which included five vents in the basement. I had an energy conservation expert from the local electric company do a survey of the home. He suggested that I seal off all five vents in the basement since there was no living space down there. A little later my HVAC expert came to examine the system. He said I needed to keep those vents open as the system was designed to move air through those vents. Otherwise, I was building up too much pressure, causing extra strain on my HVAC system. What's the best way to go? How can I be the most energy-efficient and save money in the long run?
Generally speaking, shutting off registers should not add any kind of strain to the system. One thing to be aware of with respect to basement ducting: Make sure any return registers are left open because that pulls air back to the heating system to be reheated and re-cooled. That would include any damp air in the basement, which keeps the basement drier. One caution with regard to basement returns: An HVAC expert should make sure they're not located too close to the furnace, as that can cause the room to depressurize and combustion gases to be drawn into the house.
With all that said, I don't expect you to get a significant savings on AC by shutting off the basement registers because the thermostat that controls whether the system is on or off is most likely upstairs, away from that room.