Consensus, no. There is hardly any consensus regarding the biographical Shakespeare and the plays by the man of the same name. Heck, there is not even consensus that Shakespeare was the author of his own plays! Many have made the assumption that Hamnet's death had much to do with the writing of Hamlet (the names do sound the same, don't they). But one should be wary of such interpretive leaps -- a person's biography is not necessarily causation for their dramatic work.

The best summation of this issue is perhaps Emma Smith's podcast on ITunes University entitled "Approaching Shakespeare." See the Hamlet episode. All of her podcasts are really fantastic sources of historical, contextual, and critical information.