No. None at all. Kate Middleton's family descended from a purely middle class background on either side. Her family presently resides at Berkshire, few miles from London but it was reported that they originated from Leeds, England. She has no aristocratic background. She will be the first middle class woman to marry an heir to the British throne and the first woman without any title to marry into the direct family of an heir to the throne in 500 years.
No. Kate Middleton is from a common family without royal descent. She does have the English descent, but with a few Scottish and French.