They would have been wiped out from the inbreeding....
Actually the inbreeding could have made them eligible to be in the British Royal Family.
I can see the plot line now. Anthony is invited to perform at the Royal Albert Hall, and all the Corleones attend. Mary's daughter is introduced to King William's son, Michael makes a handsome contribution to the Britsh National Trust, buys Manchester United and the Times of London, pays a "visit" to Dodi Al Fayed's father who sells him Harrods for a certified check for $10,000 (either his brains or his signature would be on the contract) and a Royal Wedding ensues, finally making the Corleones legitimate. Michael is made a Duke, he is knighted, and he reunites with Kay the goldigger.
