Russia gets to reinforce Cauc R1, so softening up Cauc for Italy isn’t a good reason to hit Cauc G1.
If you want Cauc, think about setting up for a Round 2 attack….in that case, it would be Italy and its bbs that would soften up Cauc I1 (unless it had to counter Ukraine), and then Germany goes for it G2. To do this effectively the G Med transport should survive until G2, where it joins the Italy fleet.