They would, yes, but obviously they're not very good about it. Everyone knows they're doing it, and on what basis, too, which rather defeats the purpose and clues people in that there is something about that message which is dangerous to the interests of the censoring party. And here's the thing: The reason everyone knows about it is that on a long enough timeline everyone posts something that offends the perpetually offended.
They put up fact-checks under a post sometimes, but what those fact-checks mean for the visibility of a post is left to your imagination. If a post or link is outright censored, you don't find out about it until you try to post it. As their censorship intruded even into so-called private messages on those platforms, even in a 1-to-1 conversation, sending something prohibited doesn't show any kind of "Prohibited content censored" message to the recipient (even non-spam).
They'd much rather you don't know they're censoring anything.