This has been mentioned earlier, but...
If you have a bathroom fan on 24/7 you are exiting warm air, and cold air is coming in from outside to replace that air. You have to heat all that cold air. Not very cost effective method.
Even if you put in a vent in the closet that replaces that exhausted air, your chimney from your boiler might flow backward and you could get carbon monoxide poisoning. You should talk to a heating specialist.
You want to have + pressure in a house, not negative.
Once you get the pressures figured out, there are humidity control units that will only start the fan at a preset humidity level.
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