Sometimes restaurants will waive acid age fee for either wines that don't have on their menu or for wines purchased at a local store. Obviously, CA Grill doesn't have any associate wine shops, but I'm sure if you want to bring a special bottle they'll make accommodations and charge a corkage fee. Expect $25/bottle or so; that's the going rate at "real world" places. Let us know how it works out.
Thanks. I'll let you know if we try it. I'm not sure I want to fly with the bottle but we'll see how set my husband is. His boss recently bought a couple of wineries in Italy. So he was thinking about bringing along a bottle of their sparkling wine to start the meal off. We're celebrating my moms birthday that evening. Worse thing that can happen is we enjoy it in our room (BLT) before dinner and order another bottle at dinner. And we may end up preferring to do that anyway.
We did corkage in Remy and Palo on Disney Cruises so my first reaction was why why would it be any different in resort restaurants. But a quick google search came back with mostly DIS Board threads (so take that for what its worth) but it appears while V&A, Artist Point, and some others do do corkage - CG does not (as of the most recent post from beginning of 2016). Suggestion: call Disney Dining and ask specifically about CG and corkage if you want a definitive answer.