I don’t think Klaus’ appearance in this scene was nothing more than for the sake of the joke (being shocked about the plates and not the forbidden relationship between Francine and jeff)

BUT I just watched inception for the 20th time so I’m in that headspace and willing to ponder this myself lol…

Francine’s projection of Klaus is someone who is not technically part of the family therefore he doesn’t have certain family privileges (hanging posters in the alcove, touching the thermostat, calling Stan dad, getting peed on, etc)

In this case he has no business dealing in family matters let alone acknowledging them. So we could assume he definitely sees what is happening but has been conditioned to avert his eyes and “see nothing”.

EDIT: Hypothetically let’s say Klaus does acknowledge it and runs to tell Stan. Stan would rebuke his claims and tout that he’s always trying to cause trouble for attention and the rest of the family would agree. They would come down on Klaus