Yeah it makes sense, especially because in canon Saurtobi couldn't stop Orochimaru from leaving, or kill him, due to still caring about him.

I think the Hokage was truly worried that Naruto was going to get hurt by Orochimaru, but that conversation in his office probably went a little way towards rebuilding the trust that used to be there between them. Though it'll take a lot more to get their relationship back to where it used to be, it's a start.