No, bad faith is quite a different thing.

The point behind belief in belief is that one sincerely believes oneself to hold the beliefs they defend. It is rather inconsequential to them that there are viable challenges which, if rightfully considered, would provide ample evidence that countered a given belief--this because they believe more strongly in their possession of belief in a given belief than in the belief itself. Hence, they can anticipate the ways in which evidence might be presented to counter the belief and, in an effort to save the belief and for the purpose of continuing to believe in the belief, they can explain away the weaknesses of the belief in question. Fundamentally, the power in this state is that one continues to consider oneself a "believer", capable of suspending belief in the problematic belief, but choosing not to so as to retain their status as a "believer". It is important that one not seriously question their beliefs--by which it is meant to seriously consider evidence that supports their beliefs and, when such evidence is found lacking, to abandon or downgrade the binding power of their beliefs until such beliefs are warranted by evidence--because that way lies the path of unbelief.

Bad faith, on the other hand, presents itself in conscious form in which one acts inauthentically against one's own interest, against one's stated principles, or against one's conscience (and consciousness). It is the doctor who really wishes to be a pilot continuing to practice medicine because that is his currently chosen path. This is frequently a result of the denial of one's conscious freedom to determine one's course of action. Instead, one who operates out of bad faith disassociates oneself from one's actions, or claims to possess more limited choices than one actually does. For Sartre, there is nothing about human nature that is predetermined; there is no "true self" over which one possesses no power. We are human consciousness built over time by actions we freely choose--and too frequently according to roles, beliefs, characteristics, or modes of action others have given us.

In the 1976 documentary, Sartre by Himself, Sartre goes after intellectuals as specialists who apply human knowledge to questionable purposes determined by a political establishment. One of his examples is scientists who work on the atomic bomb. Another is professors who teach only a small group of wealthy or otherwise advantaged students. Such intellectuals may sign petitions, advocate for the working class, or engage in other kinds of actions to relieve their consciences, but never seriously question their own complicity in their own actions. They play their given role, telling themselves they can do nothing about it, and settle for having an unhappy conscience because it provides them something to denounce.

So, bad faith typically ignores the freedom and transcendence of consciousness, telling us we cannot be that which we are not. Those who lack a sense of the real in their lives might also exhibit bad faith by denying the facticity of life--asserting they can do anything by wishing it.

In contrast to belief in belief, those who are acting in bad faith would suggest they cannot believe otherwise, perhaps because that's just "who they are" and that they cannot do anything about it. But believers do not suggest such a conscious position. Instead, they reject any efforts that might diminish their belief in their beliefs, because maintaining belief is, for them, of the highest good. They are, to varying degrees of understanding, aware of evidence and claims that counter their beliefs and, were they to be persuaded by facts, might lead them to abandon the belief. But they cannot, not because they have chosen a factual position that has proven their beliefs, but because the act of believing in those beliefs provides the truer source of defense.