Most ACA tours start out at a motel, so I would assume you could ship your bike there. Must be quite a challenge, however, for the motel to receive and store so many bikes at one time. Better call and verify. If the motel cannot receive it, a local bike shop almost certainly can (especially if you pay them to put it together for you).
Depending on the airline you choose, it may or may not be a good deal to bring your bike with you on your flight. If you're flying Frontier or Southwest, it is usually feasible to bring your bike on the plane. If you're flying anything else, it may be more economical to ship it. Also, depending on your preferences, it may be more convenient for you to ship it, or more convenient to bring it.
If you're going on a loop tour and book your first and last night with the same hotel/motel, they are usually willing to hold your box. Call and ask. If this is a one-way tour, you'll probably just want to ditch the box.