Finally had time to do the back and forth emails with DCL regarding gift basket deliveries. Short answer - No
Below is copied and pasted from their email response:
"Items that cannot be delivered to the ship include: food products (all and any food products), baby food/formula (unless shipped through Babies Travel Lite), beverages (liquor, water, etc.), chemicals and luggage. . These items will not be accepted at the warehouse and will be returned.
Disney Cruise Line does not prohibit Guests 21 years of age and older from bringing alcohol onboard. However, please be aware these items must be hand-carried onboard in a day bag and/or carry-on, which cannot exceed 22" x 14" x 9".
As far as coolers, large coolers may not be brought onboard. However, small personal-sized coolers for the purpose of housing medications, baby food, baby milk, or items related to dietary constraints are permitted to be brought onboard. These coolers can be no larger than 12" x 12" x 12" and can only contain the above items.
Please be aware, though, Guests are unable to consume alcohol that has been brought onboard in any lounge or public area. Hard liquor or spirits are not able to be to be taken to the bars or lounges for the bartenders to prepare specialty drinks.
Guests can still take a bottle of wine or champagne to the restaurant for dinner. If you request a Wine Steward to open and serve a bottle of champagne or wine that has been brought onboard a corking fee will be charged per bottle.
If the Guest opens the bottle in the stateroom and brings it into the dining room, they will still be charged a corking fee.
Please be aware,
Disney Cruise Line reserves the right to remove fragile items (including beverages) from checked luggage. The items will be stored and returned at the end of the voyage. Beverage containers are considered fragile and in checked luggage have caused damage (e.g. carbonated cans "explode", glass bottles break). For this reason, all fragile items and beverages must be hand carried by the Guest onboard the vessel in a day bag and/or carry-on. "
I'm going to pass this information on the Gift Basket Overseas to see what kind of response I get from them.
I was hoping to avoid having to carry on the liquor and mixers since we usually have our hands full getting the elderly folks on board with the wheelchairs. Maybe I'll make Mom hold it in her lap.
So thanks for the suggestion to check with DCL.