First, it is necessary to dispute the use of the “subplot” in describing pride and prejudice in Austen’s novel Pride and Prejudice. “Subplot” is defined as a story line built upon conflict that centers around a supporting character (e.g., the romance between Jane and Bingley or the marriage of Charlotte and Collins or the story lines that center around Wickham). In contrast, theme is defined as the central unifying idea upon which the entire work is founded. In this case, Austen’s Pride and Prejudice is unified around the central thematic idea of pride and prejudice. Having pointed this out, I’ll follow up with an answer that utilizes the term “subplot” instead of “theme,” as the end result of the discussion will be the same.
Conflict drives the plot by definition: “Conflict is the engine that drives a plot” (Wheeler). The conflict in Pride and Prejudice is Elizabeth's prejudice and pride and Darcy's pride and prejudice, which produces their misunderstandings and fuels the conflict, which by definition drives the plot.
She is tolerable; but not handsome enough to tempt me; and I am in no humour at present to give consequence to young ladies who are slighted by other men (Darcy; Chapter 3, Vol. 1)
It is pride and prejudice that form the foundation of the thematic concerns of the rising middle class of newly wealthy tradesmen, like the Bingleys; wealth, social class, and prestige; and love and marriage, especially prejudice in love and marriage (e.g., Elizabeth's prejudice against Collins and Rosings versus Charlotte's humble acceptance of the same).
If the subplot of pride and prejudice were removed, some other basis for Elizabeth’s and Darcy’s determined misunderstandings (especially Elizabeth’s) would need to be supplied. In order to keep the plot in tact, this new basis for misunderstanding would need to be flexible enough to encompass the thematic elements of new wealth, prestige, and marriage detailed above. Perhaps there is some subplot that could stand in lieu of pride and prejudice that would not significantly alter the thematic and psychological dynamic, but those I think of alter the psychological dynamic beyond recognition. One might give Darcy a serious personality flaw, like a pathological degree of shyness, but that would add a negative psychological component and dependency that would radically alter the nature of the characters and the novel as a whole (Lydia and Mary might come out looking like the psychologically stable characters!).
So, on one hand, yes, if the subplot of pride and prejudice is removed from Austen's novel, the plot can develop: there can be balls and Charlotte's marriage and Jane's ruined romance and the trip to Derbyshire and Lydia's fall from favor and the reconciliations. On the other hand, no, if the subplot of pride and prejudice were removed from Austen's novel, the plot could not develop in the same way with the same psychological and thematic outcomes.