Only if you promise not to wear your shorts if your luggage does arrive
I have asked many times how many people have not gotten their luggage before dinner time and not gotten too many people telling me they did not. Of course, just by looking at the number of people in shorts at dinner the first night, you would think it would be at least 1/3 to 1/2. My observation is tempered by the fact that we do the early sitting for dinner. My feeling is that many people get caught up in staying up on deck to watch the ship leave and then with the muster drill (or reversed) run out of time to change for dinner.
We always just pack some slacks or skirt to wear the first night at dinner in a carry-on. Sometimes, we've had our luggage and that would not be a problem, but you can't count on having all your stuff when dinner time comes around.
I've done Carinval twice to Mexico, and I would have to say I don't think shorts would be appropriate for the main dining room. On the positive side, I've never had a problem getting my suitcases in time for dinner either.
I think Pamda recommends packing something in your carry-on, but I never have room, so I just chance it.
Most of my women friend who travel with me usually opt for a nice pair of slacks and a top with some simple detailing for the first night dinner.
I wear a pair of slacks on the plane and carry a nice top in my carry on just in case the luggage is lost or late. I remember most people ended up wearing shorts even for the 8:30 dinner seating because many didn't have luggage yet. But that may depend on the time of embarkation versus the time of dinner and the number of passengers on the ship.
Planes and airports usually tend to be rather cool, so I usually wear slacks and a shirt with a collar when travelling anyway. Thus, I'm "good to go" as far as dinner the first night is concerned.
In the past, we have always recommended taking a couple changes of clothing in one's carry-on luggage so that one would have it if needed. Unfortunately, the aftermath of "9/11" has complicated this with severe restrictions on carry-on luggage (now limited to one piece plus one personal article such as a briefcase, a laptop computer, or a purse). Fortunately, the baggage handling system seems to have improved dramatically so missing luggage is quite rare now.
On our first cruise (on Carnival), I got caught by not having my baggage delivered yet. I called and asked if shorts were O.K. in those circumstances and was told to go ahead and go in my shorts. I did get disapproving looks though.