with a return in the basement and the fan running all the time its going to mix the air throughout the house more evenly. Therefore if the basement is the only spot your having humidity problems it will help out. It may not be perfect but it will be better. Its probably the most cost effective solution to your problem. If you want perfect be prepared to spend $$$.
It'll work fine if you add a return register. No need to run the fan on all the time, that just adds unjustifiable electrical costs with no added comfort. If it's too moist down there, find out why instead.
You didn't indicate whether your basement is finished or not. Moisture in the winter is not a common problem and 50% RH is not a problem either. In fact, most homes seeking comfort will run 40% - 45% RH in the winter and 50%-55% in the summer.
If your basement is finished, you can try controlling the humidity with the main system as others have suggested with supply and return air. Once you open the basement to the rest of the home, you'll find the moisture moves lickity-split to the rest of the house. Absent moisture barriers, it's nigh on to impossible to contain moisture. It flows very quickly to the drier air.
If you don't get satisfactory results with the supply/return issue, I'd highly recommend a whole house dehumidifier dedicated to just the basement. With that arrangement, you'll be able to control the humidity both summer and winter in your basement. I would think summer would be a huge problem if you're experiencing a problem in the winter. A whole house unit dedicated to just the basement would solve your problem unless you've got standing water.
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Agree with the redistribution of humidity. Also agree that if it's nearly a problem in winter, it should be a large issue in the summer. Would strongly suggest radon testing before you decide to redistribute that along with your humidity.
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