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Yes, it is quite possible. Children have a chance to inherit the culture of: a) their father, b) their mother, or c) the capital's local culture. I think it's something like 70%, 15%, 15%, but I can't recall off-hand.
 
It's certainly possible. Every child that is born has three possible sources from which to inherit its culture. They can get their fathers culture (most likely), their mothers culture (less likely) or the culture of their home province (least likely). I'm not sure about the percentages but I would guess they are something along the lines of 65% (male inheritance) 25% (female inheritance) 10% (province inheritance).

In my last game as Jerusalem, the ruling branch of the de Normandie dynasty turned saxon in the early 12'th century only to turn swedish a couple of generations further down the line. Then again, that game included the Republic of France running wild amongst the italian city states and a swedish King of Seljuk Turks so it wasn't exactly the weirdest thing that happened ;)