Depends on what you're trying to accomplish with the fast. If the goal is gut rest, you're probably breaking the fast to some extent.

As for autophagy, as far as I know there are no good biomarkers to determine autophagy levels, so it's hard to say whether black coffee stops autophagy, or even whether you've entered a state of increased autophagy as a result of the fast, regardless of length or methodology. It'd be great to have some, though.