What kind of role does the content of the preface play in connection to the drama?
Yes, it guides us to take very seriously the play’s criticism of capitalism, marriage, and the position of women in Shaw’s 1895 British culture. He wants his audience to understand the significance of his play, he wants it in fact to be a “sudden earthquake” that “shocks” the foundations of morality,” sending people “into the street shrieking that the pillars of society are cracking and the ruin of the State is at hand.”Although he says this ironically, the audience should not be fooled by that tone, for indeed Shaw, a Fabian, would like nothing better than “to crack the pillars of society,” represented in the play especially by Crofts, whom the stage directions describe as “a tall powerfully-built man . . . fashionably dressed…. Clean-shaven bulldog jaws, large flat ears, and thick neck: gentlemanly combination of the most brutal types of city man, sporting man, and man about town. (Act 1)
In a sense you've answered your own question. Shaw, as you know, loved to write lenghty explanatory prefaces to his plays, explaining his philosophy, what he viewed as the social significance of his work, and so on. But in as much as these prefaces were often written well after-the-fact, arguably they are of no more importance than the analysis of any other critic. In other words, Shaw's word is not necessarily the last word.
Morevoer, 100 years of productions of his plays have shown that these wonderful prefaces add nothing to the actual performance. Shaw was a brilliant dramatist, and a brilliant critic, but dramatic criticism doesn't play on stage! Shaw himself is reported to have told an actress, "Never mind what the speech means, my dear. You read it beautifully."
So - I suggest you take the view that the preface to "Mrs. Warren's Profession" adds an interesting perspective on the play, but you have to take Shaw's comments on his own work with a grain - or two - of salt.
I hope this is helpful.