Yes. Other examples are Metformin, Minoxidil, and Modafinil. Prescribed to millions of people and we only have guesses about how they work. Another very interesting example is thalidomide (yes, that thalidomide). It was approved in 2006 for cancer use in treating multiple myeloma. It wasn't until 2014 that scientists finally understood the mechanism that shrank the tumors. It was so successful that it doubled survival rates.

Yes, Tylenol's molecular method of action has never been experimentally confirmed.