There are lot of issues with this question.
Is it a finished basement?
Is it well maintained?
Clean or dirty?
Bricks or Dry wall?
Any windows?
Carpets?
Where dirt, dust, bad air and other particles in the air. Affect the quality of the air. The removal of the moisture from the dehumidifier can't really cause much problems to the equipment.
Avoid storing equipment in non dry areas.
Plastic Bags
Material bags with plastic lining
Wetsuit, protection guard, socks, gloves etc.
Ensure that it's clean and dry prior to storing.
BCD
Apply disinfectant around the valves of the inflator hose and the air release. Ensure that it's clean and dry. Free from salt water crystal. Follow factories guidelines.
Regulators
Disinfect the mouth piece and the surrounding. Rinse very well, and let dry completely.
Store in a closed and dry place. Allow ventilation every week or so. Never hurts. If your going to store for a long time. Wash, rinse and dry your equipment every couple of month or so. To prevent from really driving or freezing up or other climate conditions that arise.
Think of this similar to things not used for a while. They tend to be in a state that require re-awaking. Keeping them active maintained preserves the life of the product or item.
"Keep your items well and they'll serve you well too." Have fun diving...