Yes they do.
They are a very large-keeled duck; some of the show-bred ones have trouble, er, breeding cos the poor gents are unable to balance!
The last supplier of pure-bred Aylesburies in Bucks is here in Chesham - his name's Richard Waller and the ducks are amazing*. Rick Stein did one of his local heroes shoots there. They don't give them much in the way of water to swim in, because it makes them get fat rather than muscular (think of insulation). I think they just dabble about. But yes, the pens do get incredibly muddy, especially when there's a few dozen in a hatching. http://www.chilternsaonb.org/site_details.asp?siteID=258
I still can't believe the family have been there since 1775!
Down by the Chess, the local mallards cause havoc in people's gardens, as they waddle over everything and destroy plants.
Ducks aren't easy garden companions! (Doesn't stop me wanting one, though). Yours will be full sized at 10wks and they are *not* small ducks!
*They taste rather good, too! Must phone them up and order another...