Dryhopping doesn't add any hop FLAVOR, just aroma. There's no alpha acids being isomerized so no flavor is going in.
Kaya, you're not the first person that's contemplated it or done it. Or flavored their priming sugar with ginger, or cinnamon or other spices. I've done it. It will work.
Are you gonna strain them before dumping the solution in? I would. Just let the whole shebang steep. In fact boil your solution, then after a couple minutes boiling. Turn the flame off, throw a lid on the solution, and let it cool for 15 minutes or so, that way any of the aroma oils should fall back into the solution as condensate.