I'm hearing that SPDY is where things are likely headed, and I'd like to try to use it with a Rails site I'm running. I haven't been able to find any tutorials however, and the one gem I found doesn't seem to work (everyone is reporting the same error on it across all browsers).
Is it currently possible to implement SPDY on Heroku with a Rails app?
No, there is no way to get SPDY on Heroku today, although I do hope that will change in the future. Heroku has their own HTTP "routing fabric" which is fronted by nginx frontends. The nginx team is working on a SPDY module, but there is no hard date for its release yet. In addition, Heroku would need to install it on their frontends, etc -- in other words, it would require some careful coordination.
If you are interested in testing SPDY with Rails, I would recommend checking out mod_spdy for Apache. You should be able to use Passenger in conjunction with mod_spdy, although that would have to run outside of Heroku for now.