Yes, but the preachiness is presented as deeply lovable. Even someone as bolshy and sparky as Jo is reduced to floods of filial tears by some repellently preachy letter from their father about his ‘little women’ making him proud..
All the girls are depicted as having to be preached at and cut down to size — poor Meg, with her hardly unnatural thirst for dressing up and the occasional bit of fun rather than sharing a pair of gloves and giving her breakfast to the Hummels on Christmas Day, gets taken to task by the younger, spectacularly wealthy Laurie for once drinking champagne and wearing her friend’s nice dress.
Jo is rebuked by Professor Bhaer from trying to make a living by writing pulp fiction.
Amy only bags Laurie once she’s given up her selfish artistic ambitions and become all patient and womanly.
Even Marmee is lectured about her temper by her ghastly husband before he disappears off to war, leaving her to raise four children on a shoestring.
Only Beth is perfect, because she never has any desires whatsoever other than dusting, playing the piano and hanging out with the cats.