A few caveats: "Current implementation of SPDY protocol does not support “server push”. Processing of requests from SPDY connections cannot be rate limited." http://nginx.org/en/docs/http/ngx_http_spdy_module.html
And SPDY doesn't support caching per default. Well, it's hard.
Can you clarify this statement? Perhaps there's missing context, but as it reads, it seems like a false statement. When I look at chrome://view-http-cache/, I see a bunch of https:// resources for google.com (which are served over SPDY).