The fact that the RX48-0 still see a big boost when using async shaders merely suggests that AMD still have major problems achieving anything close to 100% utilization under DX11 and so the architecture improvements in the new GCN 1.3 are pretty minimal, which si backed up by the lack luster performance.
The fact that Pascal doesn't see a bug improvement with async shaders is much less interesting than the fact that the RX480 does. IMO.
AMD will never achieve 100% utilisation in DX11. The same goes for OpenGL. This was a decision AMD made a while back and it is not going to change. It was all about COST: the didn't have enough money to develop top-notch drivers.
Think about it like this: if it costs $100 to produce a card that you sell for $150, then your profit is $50 per card, right? But that's not the end of it. You need to release drivers. Let's say you sell 1 million of those cards over 2 years. That's $50m profit. But how many man-hours of software development do you spend over those two years to make drivers and optimise per game, or to 'sponsor' games so they work well on your cards? If this costs $40m then you're left with $10m profit. These are random numbers but I'm just trying to make the following point:
AMD decided that it can't afford to pay $40m for drivers/sponsoring. So DX11/OpenGL fell back compared to NVidia and the latter was much faster. What did AMD do instead? They said let's build cards that cost $130 to produce but still sell them for $150. After selling 1 million of those cards we'll have $20m profit which is more than $10m we'd have by investing in DX11/OpenGL. Basically they threw more hardware at the problem to keep up with the better NVidia performance (due to better NVidia software) and even then their cards lost on average. When you compare like for like (e.g. GTX1060 is at 4TFLOPS vs RX480 that is over 5TFLOPS ) the AMD card has more processing power but the NVidia card is still faster in DX11/OpenGL games (it's only because of the extra processing power that the AMD card can stay close).
Enter 2016: what is (finally) changing is that games are starting to support DX12 and Vulkan. As games start using these new APIs, the disadvantage of AMD drivers is removed and furthermore the 'extra unutilised hardware' starts getting utilised. This is true even for older AMD cards.
So basically, async compute is just a small part of the equation and the reality of DX12/Vulkan is much more complex. Async just gives an extra advantage to AMD for certain workloads (which are actually not rare, so it's significant).
As far as the original question (should I still get a GTX1080 after seeing how well the RX480 does): if you can afford the GTX1080 then it'll give you the best performance right now. It is in a different class than the RX480 so even with async/Vulkan/DX12 the RX480 will never get close to the 1080.
Is the GTX1080 a good investment? Not so much. It's way overpriced because there is no competition for it since Vega is still 6 months away.
You will enjoy the 1080 for the next 6 months. Once Vega is released, you will start thinking that you paid way too much for it. But if money is not an issue for you, it won't matter that much.
EDIT: like other people pointed out, there's also a 'missed opportunity' cost. With the money you sacrifice on the 1080 you could instead invest in a better monitor or CPU or whatever. I would seriously consider their advice. Lots of good ideas through above (e.g. an RX480 with a FreeSync monitor combo).