Well, most any kind of asset has some diversification value. I see no particular reason for BTC to be countercyclical (not to mention that the traditional business cycle of the late XX century seems to be dead at the moment, or at least much transformed) and in any case there's too little data to tell.

And if you think BTC has some extra special value because it will be {un|low|negatively} correlated to the S&P then you need to compare it to a different reference class.

With respect to the probability distribution, no, you were right the first time -- we're both talking about the probability distribution of the value of 1BTC at some long-term point (and you really should define what does "long-term" mean here, in years, for obvious reasons). I'm not talking about hyper- or meta- distribution of your credence.