Hmmm. Not quite. The only reference to Rolex watches in the James Bond novels is in On Her Majesty's Secret Service and no specific model is named, only a 'Rolex Oyster'. As for the Submariner that Sean Connery wore in the original movies, it was Ian Fleming's own watch, which he bought with the proceeds from the sales of the novel On Her Majesty's Secret Service, co-incidentally....
Regarding military issue watches, both Rolex and Omega have been specified by British Forces (where do you reckon those reps with the little 'T' on the dial get their inspiration from?!)