Not sure why it is called Georgian chicken, but that is beside the point. I think every culture has a chicken similar to this. I wouldn't worry about rice color. The Color of the cherries would be much stronger than cranberries. The only concern I have from reading the recipe is rice stuffing. Basmati rice cooks really fast, and in my opinion will be ready in 15 minutes, id it is going to seat in the oven for another 2 hours, it’s going to became a mush (is it a word?). I do always precook my rice for stuffing but I use rice that cooks much longer compare to basmati rice.
Game or a small bird will have very small cavity so there will be very little room for the stuffing.
You are what you eat.