I don't know too much about the FAA system but I would surprised if they did not.
I know a person who is the holder of a JAA class 1 and his AME told him blood pressure reducing medication is accepted by the JAA to help reduce blood pressure as the side effects of these drugs are not as adverse as in earlier years. I would suspect the JAA would need to be informed though. With the better drugs the effects of high blood pressure is much undesirable than side effects in most cases.