With sugar, alcohol and acid, I wouldn't worry too much about infection.
Your FG will likely drop, but you'll have to calculate by how much. It shouldn't be drastic but from 1.012 to 1.010 or something like that, you're adding pure sugar that's 100% fermentable. It will boost your ABV as well, but again, not by much.
I'm going to guess that the 3 grams of sugar is a "per serving" statement. There should be a lot more than 3 grams of sugar in a 1 pound jar of cherries.