I think this would be a great place to live and downtown Austin is great. Whole foods is right down the street, and my favorite lunch place (austin java) is across the street. I would move there in a second. Taco shack is a little far away at 3 blocks, but I could make it work. Oh I miss Austin.
Ok, so back on topic. I would bet that your treatment at this property and potentially other Ws would be enhanced and that you would get some level of special treatment (not sure exactly what but definitely something.)
However, I bet the special treatment at the other SPG brands is very low. Otherwise, why would they not just make the purchasers platinum, instead of the very low value gold status. Basically, if the owners of the hotel had the power to get other properties to give you benefits at the platinum level or higher, I would think they would have been able to get their purchasers platinum status.
Also briefly reading about time-share owners, it doesn't seem like they get any special treatment outside of their home property and I think this would be a similar case.