As the link you cite points out, the law of large numbers stipulates that in statistics, "as the number of identically distributed, randomly generated variables increases, their sample mean (average) approaches their theoretical mean."
So unless you are saying that sustainable interaction is the theoretical mean of the fecundity of nature (in the broadest sense possible, encompassing the initial conditions of the universe) then it is difficult to see what the law of large numbers has to do with it.
It almost seems as if you are saying that given a sufficient number of random events anything and everything will happen, but not only doesn't the LoLN specify that, but I would like to give you more credit than that. Sustainable interaction is a human story we project upon nature given our experience of it. To say that it must necessarily arise imposes teleology, and therefore an overall mind (read "God") on the universe.
I am reminded of the error of the creationists, who insist that evolution by natural selection is like expecting a hurricane blowing through a junkyard to produce a commercial jet liner.