Well Jane, you hit a nerve, 9 pages of replies so far! Your post took me back to a lovely holiday we had in Italy, years ago, when at the 2nd location (Merano) of two centres we were in a rather posh hotel. A couple of ancient German ladies used to do exactly what you describe, they brought huge handbags to b'fast, and smuggled away as much extra bounty as they could, mostly fruit. After they'd gone, the waiting staff were clearly having a chuckle about them, as were other guests.
You could actually check with the head waiter, but I expect they see that kind of thing all the time, if the buffet is really big enough to satisfy Americans on a cruise ship?!