Nope. Mardi Gras class only has inside, ocean view, and suites without a balcony in the Family Harbor section on deck 4, which is the lowest level passenger deck on the class.
Vista class has cove balconies in the Family Harbor section.
I can confirm having been turned away from the Steakhouse on Mardi Gras last year. My then 15yo son was wearing nice shorts and a button-down shirt. We were told he could not enter wearing shorts. We ran to the room quickly and changed. No big deal, but it did happen.