Although turnout in the primaries does not predict turnout in the general election, the party with higher primary turnout does enjoy one benefit in the general -- the votes of people who had sat out the previous election, but are showing up this time around.
Here is primary and general turnout (in millions) since the 50-state primaries became the norm in 1976:
In years when both parties ran a primary, the Democrats had higher turnout in 1976, '80, '88, '92, and '08. The Republicans only had higher turnout in 2000 -- and now this year as well.
The party with higher primary turnout doesn't necessarily win the general (see '80 and '88). But higher primary turnout does show up in the general as a bias toward that party among the infrequent voters (who did not vote last time).
Here is how the infrequent voters compared to the frequent voters (who did vote last time), where positive values show a greater bias toward Democrats, and negative values a bias toward Republicans.
Compared to frequent voters, infrequent voters showed a bias toward Democrats in '76, '80, '88, '92, and '08, while they showed a bias toward Republicans in 2000.
This predicts that, since the Republicans had higher primary turnout in 2016, the infrequent voters this year will vote even more Republican than the frequent voters will.
What about crossover voters? Their bias, compared to partisan voters, looks highly similar to the infrequents compared to frequents. But in 1980, the crossovers voted more Republican, while the infrequents voted more Democrat. So the party with larger primary turnout almost predicts which direction the crossover voters will head, although not perfectly. Still, it's a strong relationship, and the prediction this time is that crossovers will favor the Republican more than the partisan voters will.
We've already come to these predictions after looking at the history of crossover and infrequent voters in the general election. But now we have another source of confirmation -- the outcomes of the primaries.
Clearly Clinton will win among partisan voters since Obama beat Romney, and Democrat affiliation is higher than it is for Republican. But with substantial crossover (the main effect) as well as a minor boost from infrequent voters, Trump is set to win in the overall electorate.