Given that the only child available to me is my 21-month old, I would say "Yes" 
But, less facetiously: if you asked a child in Samoa on 2011-12-29 what the date would be tomorrow and they said 2011-12-30, they would be wrong because the following date was 2011-12-31.
My point is, if you're asking "what (year, month, day) does the Gregorian calendar by definition specify comes after (year, month, day)" then there is an answer that can be given by that definition itself — but this is rarely a useful question, or answer, and is not what most people are asking. It's useful if you're, for instance, laying out and printing physical calendars; but if you were to ask someone "hey, what's tomorrow's date?", the answer does depend on the time and day you're asking, yes.