Williams has the reader learn about Blanche's true history while she is out of the room. How does that dramatize or heighten the suspense of the succeeding scene?

By keeping Blanche out of this denouement, Williams heightens the suspense of the succeeding scene. Everyone knows the truth about Blanche now – the Kowalskis, Mitch, Blanche, the audience – and all that remains is for Blanche to know that they know. In a play like Streetcar where much of the action has occurred off-stage in the past, it is an effective dramatic device to have the audience know more information than the protagonist. This device camouflages a lack of action and lends a drumming inevitability to the succeeding scenes, while elevating the meaning of everyone's actions – we know what they're thinking, and we are just as tense about it as they are.