Hi, I'm Dr. Bonk. I"m sorry to hear about your dog's troubles. Advil can be toxic to dogs in large enough doses. Typically toxicity occurs if more than 300 mg per pound is consumed or after numerous doses over a long period of time. The most common symptoms are vomiting, diarrhea and decreased appetite.
If you are at all worried that he may have ingested more than just the coating, you can try to induce vomiting using hydrogen peroxide at 1 ml per 5 lbs body weight. Give this dose then wait 5 minutes and repeat if needed to induce vomiting. This can be repeated up to 3 times.
If you think he just got the coating, you can watch him for signs of vomiting, diarrhea, decreased appetite, or lethargy. You can try giving him a small meal right away to slow absorption and offer him plenty of fresh water.
If he starts showing any of the above signs, or just seems off to you in any way, it would be time to get him to a vet.
I hope this helps. Please contact me with any further questions you may have. Thank you and good luck!