Yeah, Gaara's son has the 3rd kazekage's KKG which means they're from the same lineage
Alright, I found what you mean, but I don't think its exactly what was said in the novel. Gaara's father already had Jiton, though it was never mentioned his grandfather was Kazekage. Still, being a descendant of a kage is a good way to get credit, allowing you to be more inclined to be picked as a Kage yourself rather than some random Shinobi.
Examples being the third and fourth Ay's, Minato and Naruto, Kurotsuchi and Ohnoki and Ohnoki and Ishikawa, Hashirama and Tobirama and Hashirama and Tsunade and, of course, Gaara and Rasa.