Here's a good article on the distribution of DNA.
http://www.isogg.org/wiki/Autosomal_DNA_statistics Even at 8 generations, the percentage of autosomal DNA inherited from an ancestor is a small part of one percent. Mayflower ancestors are 10 or more generations away. Your chance of having any of the DNA of one of your Mayflower ancestors is infinitesimal. The chance of being able to confirm that you are descended from a Mayflower passenger by comparing your DNA to another confirmed descendant would be meaningless unless you and that descendant were already closely related and you knew that the relationship lead to the Mayflower passenger by way of a paper trail.