Yes!! He clearly cared for him since he was Rogers son. When he first heard that he had "D" in his name, Whitebeard was intrigued and later on we see him basically go to Ace with his whole crew & ship on a random island where Ace is defeated by Whitebeard.
As if, keeping the only thing linking him to his old rival close to him. As if he wanted to protect him.
"Become My Son, Do whatever you want then" - ~ Whiteboard~
Basically, most important thing is what "D" is and the explanation that Roger gave Whitebeard.