From what I gather, BH isn't quite ready yet. He said he was still grasping things that go behind the QB and WR as it pertains to playcalling and to me, that means he's clearly not ready to hold it down on his own yet. Even if he left, he would probably play himself & whoever hired him as the sole, main OC. I'm thinking this prob a short term move cuz BOB never really stay anywhere too long. Maybe he continues to help Hartline along so he can then takeover.
Whatever the case, if he's good enough for arguably the best college & NFL coach to keep bouncing ideas off of (chips won or not) then I'm sure he'll provide some valuable insight for Day in some capacity. And like you said, he may just be coming in and providing work around the "edges" and not doing a total revamp to try and run his own stuff.
Obv we won't know more til we see it in action on the field but regardless, it's all gonna be on Day. He the one who gotta live or die with the decision. Have a hard time believing he would just scrap his own entire playbook tho as he's spent mad time tinkering with it + it's been shown to work in most capacities and I've seen him call sum masterful games shortcomings be damned.