No, Kakashi can't activate/deactivate sharingan, as he's not the original owner, nor from the Uchiha clan. If Obito would give him the eyes deactivated, Kakashi wouldn't be able to activate the sharingan, it's as easy as that.
Also, I believe that Obito will play a big role in the following chapters, but he'll preserve both of his eyes, as they'll give him his true power.