From Sartre’s perspective, “is it possible” would the wrong wording. No matter the circumstances or context –i.e. modern society –it is always possible to be authentic or inauthentic. It is always a choice that you are unable to avoid.
What we might rather say is that modern society discourages and punishes authenticity –that being authentic has momentous consequences for both the individual and the surrounding society. Therefore most of us assess the consequences and choose inauthenticity. It is still, however, a choice. You can always be authentic and damn the consequences.
I was thinking about this very question recently. I currently work in a business environment –the height of an inauthentic context. One of my co-workers is leaving the job, and many people are genuinely distressed to see him go, despite the fact that he has made very little effort to win friends during his time here. I think the reason people are affected is because my coworker is an authentic personality –his real self, more or less –even in a context that does not encourage that. It certainly hasn’t made his time here easier, but it does demonstrates Sartre’s contention that authenticity is always available if you choose to embrace it.