No, in fact it'll add a lot of unwanted weight. Forks that thick are not needed for a street 600. Your chassis's stiffness is not tuned for that fork. The factory race teams use the same size mm forks, so that should say something. (though it's usually a higher spec fork)
Instead, rebuild your forks with higher quality internals (Ohlins, Racetek, etc.) and be amazed at the awesome results, like night and day really. Plus it'll be a good bit cheaper.
Your 06 comes with higher quality Showa forks. These were updated from the more hardcore 03-04 Kayaba forks. It's overall a more advanced fork and is a much plusher ride.