Although Harry overhears Snape and Dumbledore talking, they don’t mention Snape killing Dumbledore. It’s clear that Dumbledore has asked Snape to do something he doesn’t want to do, but specifics aren’t mentioned.
Here’s an extract from the script for the scene:
EXT. ASTRONOMY TOWER – DYING LIGHT (LATER)
As Harry trots up the spiraling exterior stairs, he hears VOICES coming from the topmost level and pauses, peering up through the grid-like floor above: Dumbledore and Snape.
Snape: Have you ever considered that you
ask too much? That you take too much for granted? Has it ever crossed your brilliant mind that I don’t want to do this anymore?
Dumbledore: Whether it has or hasn’t is irrelevant. I will not negotiate this with you, Severus. You agreed. There’s nothing more to discuss.
Harry stands poised, peering upward, where Dumbledore squints toward the dying sun and Snape glares at his back. Finally, Snape turns away and – before Harry can react – is descending the stairs. Seeing Harry, Snape falters briefly, then continues on without a word. As his FOOTSTEPS fade, Harry ascends to the upper tier. Dumbledore turns. Smiles.
Nowhere does Snape explicitly mention killing Dumbledore. With hindsight and knowledge of the final book/film, it’s clear to us what Snape is referring to, but Harry can’t work that out yet.
Could Harry have guessed that Snape was innocent from this fragment? I think not.
He’s predisposed to dislike Snape, and emotionally distraught. He’s not casting around for reasons to defend or indemnify Snape. If anything, he may find a way to interpret this scene as extra evidence that Snape really did betray Dumbledore.
You might be able to deduce from this overheard conversation that there is a possibility that Dumbledore’s death was planned between the two, but even this requires a level of calm that is far beyond Harry at this point. Hindsight makes this easy, but I think it would be impossible for Harry.