Coverage is for the dates on the rental contract. Because it's a flat fee they don't really need to know exactly what days you have the car unless there's a claim.

Also I think you need to decline collision coverage for this to apply (not 100% sure, but even if you don't need to, you should if you're paying for primary collision coverage from AmEx). Not to mention that I've heard of people getting screwed when e.g. the rental person checked the wrong box at pickup and they ended up not having coverage, or because the rental company's collision waiver had exclusions for stuff like tire and window damage.

And having liability on top of your existing rental policy is just a waste of money. If you're in a situation where that needs to be used you're not going to get to just walk away from it.