In short: Leave the intake alone. But in detail...
Closing the dampers does not stop all air flow. Exhaust and intake work together. If you leave the basement intake fully open, then it might create a negative pressure in the basement which could suck in air from anywhere. But, most likely extra air will be sucked into the furnace directly from upstairs because the extra air being forced upstairs is creating a positive pressure there, so the upstairs intakes will work better.
You cannot suck air from an area which has no air to give. The intake will adjust itself because you adjusted the exhaust. In short: Do not overthink the situation. You want to keep the basement dry. So, unless the basement is uncomfortable, then leave well enough alone. If the duct work is good, then your situation is good. If you need to dampen the intake to make your basement comfortable, then I question your duct work. But, it would be easier to dampen the intake than to enlarge the duct work going upstairs.
If your duct work is small and you reduce the total air flow through your A/C to much, then the coil will freeze a cease to function. If that happens, then let it thaw, clean the water mess, and allow more air to flow. Trial and error will answer all questions.
.... To answer the comment question ...
Exhaust and intake work together. The size of the room/space has absolutely zero effect upon the situation. But, when you consider windows and doors, you are thinking about air leaks, and that matters.
When I say "Negative Pressure", I mean that "The intakes of the area wants more air than exhausts of the area are giving." When I say "Positive Pressure", I mean that "The exhausts of the area want to blow more air than intakes of the area can take."
In reality, everything is a comparison between two points. Pressure, like anything else, obtains a value, negative or positive, only in comparison to another pressure. The "other" pressure I am comparing to is the pressure that would exist in the event the furnace was off.
The negative or positive pressure (subtraction result after the comparison) should be very small because there are other intakes and exhausts elsewhere that are open. The change in pressure in the room represents the extra difficulty required for the fan to push air around due to the added restrictions (closed exhausts).
In example: If you close all exhausts in half of the house, then you will decrease the intake from that half of the house because there is no air to take from there (will have negative pressure). Also, if air is forced to the other half of the house, then you will increase the intake from the other side of the house because there is more air to take from the exhausts that are blowing harder (will have positive pressure).
If the pressure is so negative and positive that the furnace can suck/blow air through a doorway, then while the door is open the pressure of both areas will move closer to zero. After the door closes, given than the furnace is still on, then the pressure difference will return.
Air does not move without a pressure difference. Our education system fails to teach us many of the most important foundational things for understanding. One being that everything is a comparison between two different things. Nothing happens without a difference. Such things are good to think about and will advance understanding of everything. Many people never consider such things because and their life and their furnace roll along just fine. People like you and I imagine such things for enjoyment and the love of understanding. The wind never simply "comes from the north" at times because the wind always travels in circles. The difference between blowing a sucking is only in the mathematical sign. They both work to move air and one cannot exist without the other. Nature requires the measurement of their values to be equal and opposite. From this fact, one may conclude that air cannot be created or destroyed.
