Funny, I don't know if it wasn't allowed but I didn't have a watch as a newcomer. I can imaginge being told not to look at it even if I had one.
As an oldcomer, it was one of the first things I bought myself too. I remember Hank had a diver's watch, and Jack had a nice Casio - I think I bought myself a gold dress watch, I also remember having a water-proof digital. It was about the only piece of status jewelry a guy could wear. Scott wore (and sold) gold neclaces, but even as an oldcomer I thought that was tacky, even though Art wore one, too.