Yes, merely having the helmets does increase the risk of concussion. Partly because a player feels natural need to protect their head so they’re willing to take risks, and partly because a helmet converts what would have been a really bad injury into just a concussion.
Ultimately, if they are serious about reducing concussions and other injuries, they’ll ban leading with the head (already done, I think) and hits to the head (already done for “defenseless” players, not sure what that means). Hopefully next is eliminating the three-point stance to further reduce head hits. Ideally they’d also find a way to eliminate hard tackles to the ground, but I can’t think of a way to do that without banning tackles entirely.