It is only harmful in the allergic, immunosuppressed, and older dogs with upper respiratory problems such as COPD, but the damage is transitory.
Most of the time the chemicals in skunk spray are just plain irritating. Once in awhile a pet or person can have an allergic reaction to it. I found I can deal with one skunk at a time but didn't so well with 8 young and angry skunks that were brought in in a garbage can. My asthma flared up.
Is your dog showing any signs of allergic reaction: swelling, difficulty breathing or swallowing? If so, I do hope you've taken him to the vet by now.