I rather suspect that -this- Harry is going to be far more suspicious than Albus supect and I don't think that'll be expected. I'm sure Harry will open a friendship with Hermione but I rather doubt he's going to open up too much about what he's doing and what he's thinking. Meanwhile, the Headmaster is going to have problems since Harry will not be near as inclined to confront Tom's spirit since they've established a modus vivendi that works. I'm certain that's going to coe as a rude shock for Dumbles should he every find out.
Meanwhile, once Harry realizes that Dumbles is using Hermione as an inadvertent spy on him, what happens when he demonstrates this to Hermione and documents it to her satisfaction? Albus just thinks he has problems now.
And so the moves and counter-moves continue as Albus tries to make his reluctant weapon conform to his will; I don't think he really realizes just what he's dealing with and I daresay that he's going to be rudely suprised when he does find out.