No.
Technically a blood relative is someone who is a first, second or third degree relative.
According to the National Genetics and Genomics Education Centre, blood relatives are classified as first-, second- and third-degree relatives.
reference.com
However, Rowling meant a first degree relative.
First-degree blood relatives include parents, siblings and children. First-degree relatives share approximately half of their genes with one another.
reference.com
We can see this in the following quote where it specifies Harry and Petunia (emphasis mine).
"While you can still call home the place where your mother’s blood dwells, there you cannot be touched or harmed by Voldemort. He shed her blood, but it lives on in you and her sister."
Order of the Phoenix - Chapter 37
So the protection charm would have extended to Lily's parents (Harry's grandparents if they had still lived), siblings (Harry's aunt/uncles if Lilly had brothers), or children (Harry's siblings if he had any).
So Dudley, as a second-degree relative would not have counted.