Yes, we have (very!) recently added the "client_shipping_method_id" variable to show which Shipping Method the buyer selected in the cart. This will show an ID number corresponding to the Rule# you'd configured for the chosen Method.
E.g. if you see client_shipping_method_id=1234, that means the buyer selected the shipping method configured in Rule#1234 in your Seller Admin > Shipping Settings > Next > Existing Shipping Rules menu.