SIMPLE ANSWER: No.
THE MORE NUANCED, LESS DOCTRINAIRE ANSWER:
If we were to take Prince William as an example, and after their royal to-do, who could deny the awe-inspiring elegance of the day (Pippa, call me), unbuttoning your coat is not consider correct etiquette.
In the case of Will and Kate, for the evening the newly-wed prince wore a double-breasted jacket for the evening to do, which one never leaves open as David Letterman eventually learned after years of complaint from men's fashion magazines.
What is correct for the double-breasted is correct for the single-breasted dinner jacket. Tuxedos look GOOD buttoned up. Why settle for less.
My rule is always this: if the jacket is too hot, get a lighter jacket.
Now, it's going to happen. When the cameras were gone and Camilla and Charles had left the young ones to rage on at Buckingham Palace, I'll assume they got down and dirty because, heck they're royals, what do you expect?
And I'm sure a few garments fell by the wayside but it is not considered a polite act. So context is everything.
If you are dirty dancing and working over a bridesmaid bodice with your teeth, by all means unbutton. I never do (unbutton that is, though undo bodices is one of my favourite past times). Standing, seated or dancing, I keep coats buttoned. But then I sometimes sleep with my socks on.
One thing to consider is what kind of jacket are you wearing? If it is one of those awful four-button jobs with framed stripes and notched lapels and accompanied by a white long neck tie, go ahead, unbutton, you look like total shite any way.