In the majority of cases, a furnace fan operating set to "on" instead of "auto" will most certainly cause a draftiness in the Winter and a high humidity in the Summer.
In the heating season, if the furnace is equipt with a "low " speed fan feature that enables the fan speed to drop when the majority of the heat has been delivered, this low speed will kick in to circulate air thu-out the home. Draftiness is not as much as with the higher fan speed.
In the Summer cooling season, the fan should be set to "auto", which will turn on when the outside compressor unit starts up ,and then when the outside compressor unit shuts off ,the fan will also shut off. This eliminates the entry of humidty that is still not evaporated from the inside coil and water pan area.