Sugar will rot (or compost if you prefer that term) over time. I don't know how long that takes but probably not real long in your climate and this time of year. I don't know if it is a brown or a green. It will probably attract certain insects, bees and flies for example, especially when it gets wet. I don't know your specific circumstances but off the top of my head I can't think of any real downside.
It's on top of the sheet mulch, and not much of it, but I have more. Hopefully it melts before the bugs come out. I guess I literally have some "sweet" soil now.
I was startled when I learned that a few years ago. I'm not sure how common it is to use molasses. It wasn't real expensive many years ago when we used it in silage but it seems like it would be real "short-term" as a fertilizer.
Well anyway, I can imagine that it would boost microbe life and should encourage those critters to utilize other nutrients, nearby. When they die, those nutrients would become available as plant food.
Mauldingardener, my guess is that your sugared mulch will decompose quickly.