Looking at some other MMOs, probably not. Actually new players won’t know what’s gone unless they look it up on the internet in an effort to get upset, which most new players in a game with a reasonable degree of mainstream success don’t actually seem to do.
It’s more like cut content becomes a barrier to progression, because cuts usually aren’t done cleanly and players sooner or later run into stuff that doesn’t quite make sense anymore because it was only really explained in cut content.
As for Sam Krieg, he isn’t really linked to the main story. Even in SWL, where you really do get sent to the lighthouse, his being there isn’t important. His most interesting mission is “Crime and Punishment”, which in case of Krieg’s death could (and should) be adapted to be a mission you go on because you find a dead Krieg’s notes (and maybe some taped recording) in the lighthouse. The same might be done for “Life Imitating Art”, though imo it’s not as important. “A Reasonable Man” is definitely just a “kill stuff” mission that could just as soon be repalced with another “kill stuff” mission.
From a “the world gets darker” pov, Krieg getting overrun would’ve certainly made for an interesting story progression experiment; how well it would have been received is admittedly a different question.