Sartre was a hack anyway. Being and Nothingness is fundamentally flawed and reads like an attempt to recapture the tradition of phenomenology with a well intentioned misreading.
Sartre was always a better playwright then philosopher.
My two cents.
As to the validity of the possibility: yes. I would add that Sartre's symptoms were mild as compared to those you might read around the web. Interesting none the least.
The metaphysical comfort--with which, I am suggesting even now, every true tragedy leaves us--that life is at the bottom of things, despite all the changes of appearances, indestructibly powerful and pleasurable--this comfort appears in incarnate clarity in the chorus of the satyrs, a chorus of natural beings who live ineradicably, as it were, behind all civilization and remain eternally the same, despite the changes of generations and of the history of nations.
--Nietzsche
Ontology has it backwards. “This ‘saying to the Other’ — this relationship with the Other as interlocutor, this relation with an existent — precedes all ontology; it is the ultimate relation in Being”
--Levinas