I took mine up the Alcan and Dalton and down the Cassiar a few summers ago (<---see sig pic) as part of a month long, 12k mile trip from the eastern US to AK, the West Coast (SoCal), then home. I used street tires the whole way with no problems, even though there were/are parts of both the Alcan, Dalton, and Cassiar that were nothing but dirt and gravel for miles. Once I got over my natural disinclination to ride on dirt and gravel - esp on an ST overloaded with a month's worth of camping gear and etc - I found I could typically maintain 50 - 60 mph on dirt and shallow gravel with no serious issues. I really preferred packed dirt to gravel, and many times even to the rutted, pitted, frost-heaved, so-called "pavement". Packed dirt tended to be MUCH smoother.
The deep, drifting, recently dumped gravel was the worst, especially if you don't see it coming until the last second. Sometimes the only thing indicating the pavement was about to end was one orange cone sitting over on the shoulder (no warning signs), which doesn't give you much time to react at the 60-ish + mph you have to maintain to get anywhere in the vast distances of The Great White North.
The only issues caused by the rough roads were a few things shaken loose (Tupperware) and a minor weepy fork seal by the time I got back to civilization. I had the forks serviced and a new set of tires mounted on my way south through Seattle, and she was otherwise none the worse for wear.