http://fivethirtyeight.com/features/superdelegates-might-not...
Briefly, it would only happen in the occasion of a virtual tie between the two candidates (average of 5% points or less across states), and only if the party insiders believe there is a strong electability case to be made:
"What you’re likely to see in close cases like these is competing claims to legitimacy, with Democratic party elites showing their bias by interpreting the evidence in favor of Clinton. Suppose, for instance, that Sanders is slightly ahead in elected delegates but slightly behind in the overall popular vote, which could happen if he overperforms in caucus states.3 Clinton supporters will argue that popular votes are the truer measure of support. More exotic options might include citing national polls (if Clinton is still ahead in them by June) or the number of states she’s won (if she’s won more than Sanders). If Clinton starts out well behind Sanders but then narrows her deficit, the elites may argue that momentum was in her favor."
If the superdegates (who are free to change their minds at any point) end up overriding the popular vote by any significant margin, I would fully expect the USA to have a republican president.