If they are near the cold air return that s all that will happen is you cycle warm air into the cold air return.
Cold air return basement ceiling.
The air flows across the ceiling in the hallway towards a larger cold air return that does extend to the basement furnace.
If there is a cold air return on the floor the warm air that would normally tend to collect near the ceiling will be sucked down into the furnace.
This pulls the air across your body.
The basement one should be on the floor not the ceiling of the basement.
Have a professional contractor install a cold air return gadget in your basement.
In the basement to avoid chimney backdrafting the return air duct should be only half as large as the sum of the hot air ducts.
One other caution is to have the cold air.
The return air vent openings need to be on the opposite side of the room so the conditioned air is pulled across the room.
To make this work the heat vents need to be on the opposite side of the room.
This tool promotes cool air circulation through duct work and other house passageways.
By putting the cold air return on the floor it will vacuum up the cold air on the floor and draw down the warm air from the ceiling.
So turn the cold air return 90 degrees through the wall so that it actually draws the air from the room next to the furnace room or from the hallway of the basement.
You do this and i guarantee you that the second floor is going to be much more comfortable year round.