Will Insurance Pay for Laser Hair Removal for Folliculitis?

Laser hair removal may be helpful, but unfortunately it is unlikely that you can get insurance to pay for it. I would discuss this with your treating dermatologist and see whether they can work with you on getting insurance pre-authorization.
Every insurance company will have different conditions that they may consider covering, and different rates that they offer to treating physicians. The truth of the matter is that even if you can convince the insurance people that this is a medical condition, they usually don't pay the treating physician at the normal rate. The payment they may offer to the physician is likely to be so small that it would not even cover the costs of paying for the laser and for someone to operate it. I doubt you'll find a physician who wants to perform multiple treatments for folliculitis below cost.
In the best case scenario, you may submit you treatment receipts to your insurance and get a partial reimbursement. Once again, I doubt you will find an insurance company willing to do that.