From an API point of view, async compute is a way to provide an implementation with more potential parallelism to exploit. It is pretty analogous to SMT/hyper-threading: the API (multiple threads) are obviously supported on all hardware and depending on the workload and architecture it can increase performance in some cases where the different threads are using different hardware resources. However there is some inherent overhead to multithreading and an architecture that can get high performance with fewer threads (i.e. high IPC) is always preferable from a performance perspective.
When someone says that an architecture does or doesn't support "async compute/shaders" it is already an ambiguous statement (particularly for the latter). All DX12 implementations must support the API (i.e. there is no caps bit for "async compute", because such a thing doesn't really even make sense), although how they implement it under the hood may differ. This is the same as with many other features in the API.
From an architecture point of view, a more well-formed question is "can a given implementation ever be running 3D and compute workloads simultaneously, and at what granularity in hardware?" Gen9 cannot run 3D and compute simultaneously, as we've referenced in our slides. However what that means in practice is entirely workload dependent, and anyone asking the first question should also be asking questions about "how much execution unit idle time is there in workload X/Y/Z", "what is the granularity and overhead of preemption", etc. All of these things - most of all the workload - are relevant when determining how efficiently a given situation maps to a given architecture.
Without that context you're effectively in the space of making claims like "8 cores are always better than 4 cores" (regardless of architecture) because they can run 8 things simultaneously. Hopefully folks on this site understand why that's not particularly useful.
... and if anyone starts talking about numbers of hardware queues and ACEs and whatever else you can pretty safely ignore that as marketing/fanboy nonsense that is just adding more confusion rather than useful information.