Keep in mind that a lot of schools will list an average time to improve, but some people excel faster. For example, there might be 12 tests and the school tests every 2 months (suggesting 2 years) but they might recommend 3-5 years or even more to get BB. If he can keep up and test every 2 months the whole way through, it might be 2 years (maybe 3, depending) instead of 3-5 or even 5-7 that it takes others.
It's also possible that the instructor will let you train for a while and test in at a higher belt or progress faster if you're comfortable with it. I think the big reason for the wait between belts is to get the martial art experience, and someone with years of experience in karate already has that.
The flipside is this. Is "master" getting a black belt, or is "master" mastering the skills. For the most part, the skills should translate well (there are a few differences, but considering TKD comes from Tang Soo Do which comes from Karate, they are very similar), and he should be able to pick up the differences and the new skills fairly well. It will probably take him longer to learn all of the forms and/or any other testing requirements, as well as getting used to TKD-style sparring. If mastery is the concern, then how fast he progresses through the belts is of less concern to the skills. He could be a green belt and feel he's gotten enough of TKD to supplement his Karate, or he could be 3rd or 4th Dan before he feels he's truly mastered the techniques.