I dont think Zoro will go back at Kaido. He will get his fight against King i guess.
Now rushing back to Luffy, after Luffy claimed he will take it from here, would just disrespect Luffy as captain, would show Zoro has literaly no trust in Luffy and would ruin their relationship. I only could imagine that if the plot would come for Zoro betraying Luffy. The captain made a decision and order.