Would it totally block the air, though, or just hamper it's flow?
In other words, if the cloth structure were large enough, could it allow a small amount of dwarfs to survive in perpetuity, or would they all perish?
I am sure it has air leaks, but the cloth structure scaled up would allow water loss in the same manner as air leaks would occur, Slightly increasing water loss for volume of air because of osmotic principles.
Although curtains, airlocks and all that would work they also restrict the airflow inside the underground area, which would have to be balanced carefully or the subjects of the cave would die. Heck, even if there were no curtains, airlocks, or anything like that the CO2 levels of a cave could rise to toxic levels.
But... There may still be a way to get some water from the air without creating a closed system.
Technically if you ran really cold desert air through a cavern at night cooling the rock temperature to say 40 degrees Fahrenheit. You MIGHT be able to run 110 degree desert air through the same cavern and have some of the water in the air condense out.
This of course all depends on the dew point and such of the air, but it is a way it could be possible using sub 1400Ad technology.
Also if you only allowed the main portions of the cavern to experience cold night time air, evaporative losses would be lowered significantly.