I'm not an AHK wizard but to my understanding, the answer is "yes" to almost every "but can it do...?" questions.

In your case, from my limited understanding it would be no problem to identify a specific button in an app and then interact with it because you would be hooking into the app's low level window title / class / handles.

AHK comes with a "spy" tool where you can just move your mouse around and it gives you low level details about every window, and then you can write AHK scripts that interact with those things.

The script would look something like:

    ControlClick, OK, "My Cool App"

That would click the OK button in a window that has a title of "My Cool App". If you Google around for "auto hotkey, click button in app" you'll find a ton of examples.