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1 month agoNo. The split unit won’t have any way to move the air through the duct or attach to the duct. And the duct is undoubtedly not designed for cold air to be moving through hot spaces which will cause condensation on the duct/ and mold in the spaces where it is run.
The only quick fix here is getting a good floor fan and put it at the top of the stairs. If i understand correctly using a fan for circulating air should be done by pulling the air (ie setting it at the top of the stairs) rather than close to the mini split and blowing the air where you want it. Running the exhaust fans should also help to do this exact thing by pulling the hot air out of the ceiling areas and allowing the cooled air from other rooms to enter the bedrooms