Our bags arrived fairly quickly - by 2 or 2:30. We were unpacked before the drill. But they say they will be there before 4:00.
Definately, if the kids swim, you'll want to have their swimsuit either on them, or in your carryon. Your bags should be to your room in time to change them for dinner, although Disney recommends a change to dinner clothes in your carryon - probably best if you wore swimsuits to board. By the time your bags arrive, there won't be much swim time before the drill, the sail away party and dinner.
Our day went:
Boarded the boat about 12:00.
Immediately got seated in Parrot Cay for lunch (that is where they were directing folks)
Registered the kids for clubs (I'd do this later next time, the line was quite long - or send one adult while the other went to the pool)
We could then get into our room (sans luggage). We had swimsuits in the carry ons, so we changed.
Swam in the Mickey Pool (well, the kids did, we sat by the pool and drank whatever rum drink of the day was being served).
I went down and unpacked when our luggage arrived while DH continued to watch children.
Safety drill
Sail away party
Dinner
Kids went to the kids clubs for the welcome aboard party (Stitch taught them to Hula), we saw Hercules.
(I've didn't really see anyone to ask to help with trays whenever we went to BBB - there were people tending the food and beverage areas, and people VERY busy busing tables. But no CMs who looked able to drop what they were doing. Perhaps the only understaffed area on the ship!)