Highly unlikely. Just no real reason to even if they could. They only have so much space and very few people would both test positive and seek treatment in enough time to prescribe it before you left the ship.
The only other option would to be buying a 24 hour block on board. More expensive per day, but if you only care about internet for 1-2 days during your cruise, that could be an overall cheaper option.
If you really want a beach day, then definitely Coco Cay. If you're impartial to a beach day, take Navigator just since there are far more Coco Cay options for future cruises than west coast. Catalina Island is neat, but naturally chilly. Ensenada is only a hair better than Nassau.
Just tell the bartender you have the NA drink package.
And since you mentioned you're in a suite, you don't use your vouchers during the suite happy hour anyway.