Can (religious) faith entail an absolute commitment to the one in whom we place faith and his word, such that one should hold that "no circumstances could arise in which I would cease to believe", (see the middle of this post, and this post and discussion) as marriage is a commitment to a person such that one intends and may hold that "under no circumstances will I cease to be faithful to this person"? Or must any rational person admit the (at least theoretical) possibility of certain things that would make it rationally and morally necessary to cease believing?
Since faith by definition is about things that we do not see to be true, there is no inherent contradiction in faith as such being contradicted by things we do see to be true, such an absolute assent of faith seems to imply an assent to the content of faith so strong that one would desire to hold to it as true, "even if it (the content of faith) were to be false". Can such faith be justified?
Consider the following situation: a woman has grounds to suspect her husband is cheating on her; there is a lot of evidence that he is; even when she asks him and he tells her that he is not, she must admit that the sum of evidence including his testimony is against him, and he probably is cheating. Still, she decides to believe him. I argue that the very act of believing him entails a commitment to him such that once she has given faith to his word, while it is still in fact possible that she is believing him though he is actually lying, this possibility is less relevant for her than it was prior to her giving faith. In this sense, after faith, the "if it were to be false" becomes less of a consideration for the believer, and to this degree she wills faith "even were it to be false".
A more detailed analysis of the situation: various persons present her with claims or evidence that her husband is cheating on her. Before confronting him or asking him if he is, she collects various evidence for and against it. She decides that since believing him if he is dishonest is not without its own evils, if the evidence that he is cheating (after taking into account the evidence constituted by his statement on the matter) constitutes a near certainty that he is cheating — let's say, over 95% probability that he is cheating — that she shouldn't believe him if he says he is not, but must either suspend judgment or maintain that he is cheating. Now, suppose the man says that he is not cheating, and the evidence is not quite that much against him, let's say, the evidence indicates a 90% probability that he is cheating, and a 10% probability that he is not. She makes the decision to believe him. Since she would not decide to do so unless she believed that it were good to so, she is giving an implicit negative value to "believing him, if he is in fact lying", a much greater positive value to "believing him, if he is speaking the truth", and consequently an implicit positive value to "believing him," (even though he is probably lying).
Going forward, she is presented with an easy opportunity to gather further evidence about whether he is in fact cheating. She must make a decision whether to do so. If she is always going to make the same decision at this point that she would have made if she had not yet decided to believe him, it seems that her "faith" she gives him and his word is rather empty. A given decision to pursue further evidence, while not incompatible with faith, is a blow against it — to the extent that, out of fidelity to him, she accepts his claim as sure, she must operate either on the assumption that further evidence will vindicate him, or that he is innocent despite the evidence. But to the extent she operates on one of these assumptions, there is no need to pursue further evidence. Pursuing evidence, therefore, implies abstracting from her faith in him. To pursue evidence because it is possible that further evidence will be even more against him and provide her with enough grounds to withdraw her assent to his claim of innocence means giving that faith a lesser role in her life and relationship with him, and is thereby a weakening of the exercise of that faith. Consequently, if that faith is a good thing, then, having given such faith, she must be more reluctant to seek a greater intellectual resolution of the case by greater evidence than she was before she had given it.
In the act of giving faith, one makes a commitment to the person and his word; if such a commitment is good, and the breaking of such a commitment bad, then the value of that faith is thereby increased. So "believing him, if he is in fact lying" becomes overall less negative than it was prior to giving faith, and "believing him, if he is speaking the truth" becomes overall a greater positive value. Believing makes the possibility that objectively what one believes might be wrong less subjectively relevant, and makes one generally operate on the assumption that what one believes will not be proven false.
These considerations don't give a direct answer to the original questions, but do shed some light on them. If even faith given to persons in individual cases and in a limited respect entails a certain unwillingness (though not an absolute and unqualified unwillingness) to act upon the possibility that one's faith might not correspond to the truth, much more so in the case of religious faith given in relation to God and the whole of one's life.