I don't think you can limit the greatness of "great" people by saying, effectively, that they are socially constructed. If you are going to believe that some people are truly exceptional, then surely this must be a quality intrinsic to themselves. Ordinary people can take advantage of, or be pushed forward by, circumstances, eg the "accidental heroes." History may, it is true, give opportunity to the exceptional individual, but others make their own history, Can you really imagine a man with Napoleon's ambition remaining a corporal all his life, whatever the political situation?
Michelangelo, Leonardo etc made their way despite numerous difficulties, and stood out among a host of lesser artists. Van Gogh was eceptional, all right - the fact that he didn't sell much says more about his customers than about himself, surely? The old axiom says that "some are born great, others have greatness thrust upon them" I think that people like Napoleon and Wellington were born great, and took advantage of circumstances. Look at their generals, who were not as "great" and in many cases not quite up to scratch (eg Murat failed to be either born great, or have it thrust upon him, wouldn't you say?)
Look at all the people throughout history who have had the opportunities of class struggle around them etc, and have significantly failed to do anything! Eg during the great crisis of the mid-19th that resulted in The Communist Manifesto, how many exceptional people stood out? Marx, Engels, William Morris, Ruskin - er - er - and a few others. Today, the struggle in East Timor, for example, has produced Xanana Gusmao, Jose Ramos Horta etc, who have given direction to events, as well as a lot of good people who have been caught up in them.
I think that the contemporary political climate may give direction to an individual's qualities, by providing a specific arena for them to act in, but it doesn't create it.