I'd suggest Act II.ii is important for at least two reasons. (1) This scene shows the desperation of the husbands, like Corey, Nurse and Proctor, to stand as witnesses for the good names of their wives and to undo, as in Corey's case, any harm they may have falsely caused their wives:
COREY: Your Excellency, I only said she were readin’ books, sir, and they come and take her out of my house ... I never had no wife that be so taken with books, d’y’understand, sir, and I thought to find the cause of it, d’y’see, but it were no witch I blamed her for--I have broke charity with her.
(2) This scene also introduces Mary's testimony that all the assertions of the "children" in which they testified to having seen "spirits" was a "pretense." This means this scene is critical to the developing plot and the final resolution. Moreover, this may the most important historical scene for two reasons.
The first historical reason is that Miller is telling the story of the atrocities of the Salem witch trials, and this scene highlights that the whole fabric upon which the trials were fabricated were "pretending." The second is that Miller was drawing a parallel to the McCarthy Communist trials of much more recent history, and this scene highlights vividly the hysteria, wrong-headed thinking and delusions of power that lay behind McCarthyism. For these reason, yes, II.ii should be part of the play: it is the crux of Miller's whole point.