Yes. Though I'm T2 and I've never had a sweet tooth (I always missed my pudding, in favour of a second helping of savories), I still crave something sweet about 20 mins after eating a main meal.
The only time I didn't was when I was on the Newcastle Diet and was really low carbing. About 3-4 days into it, the cravings stopped, but they came back when I went off the diet.
As I see it, it's a bit like when I gave up smoking: The urge never leaves you, but it only lasts a very short while. If you can hang on for a minute or two, it'll go away.