Yes, many did. Most notably, his daughter, Lady's Secret was the top filly in 1986, winning many top races.
His son, Risen Star, won the 1988 Preakness and Belmont. He won the Belmont by 16 lengths.
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A horse does not have "grandkids" but the bloodlines from dams and sires trace back so far it is nearly impossible to tell how many horses are decendents from the real secretariat.