Anwser: No, not all AGM batteries are deep cycle.

But many are.

After all, they do have a greater ability to deep cycle discharge.

Four batteries at various states of charge
Not all AGM batteries are deep cycle. But those that are perform much better than flooded batteries
In fact, AGM batteries' specified depth of discharge (DoD) stands at 80% compared to the 50% DoD of flooded batteries.

Moreover, they can charge up to 5 times faster than flooded batteries.