If you mean can you show your Blue Cross card to a doctor in Mexico, no, it is no good. You'd have to pay everything out-of-pocket and then see if your U.S. based health insurer would cover any of it by submitting a claim when you got home. It depends on the policy.
This is why I urge everyone to buy travel insurance for a cruise, and get a policy which has medical coverage as well as medical evacuation coverage. If you are seriously injured in Mexico or on some island, a medical evacuation jet to the U.S. can easily top $100,000. Many health insurers do not cover any of it.
Go to Insure My Trip
and you can compare policies and see what is best for you. Also note that pre-existing conditions may not be covered unless you buy a policy within X days of making the cruise booking (varies by insurer). Thus if you have a known medical condition and it causes a problem while on the cruise, the travel insurer doesn't have to cover payments as a result.