SGI member Kitt: If your faith is pure...it wouldn't matter what the piece of paper is inside the Butsudan. As long as you continue to chant with a heart that is pure and a seeking spirit, you will continue to enlighten your life.
Mark: This is a common delusion of those who do not have a correct object of worship. However, for arguments sake, let's say this is true, at least until the practitioner becomes aware of the truth. At the stage of practice (not yet aware of the truth) your faith may remain pure regardless of the object of worship, even believing that Nichiren Daishonin is the Original Eternal Buddha. The moment that you are made aware of the truth through the Lotus Sutra, the writings of Nichiren Daishonin, through a friend, or through one's own awakening [the moment that you learn the truth that the object of worship is not a representation of Nichiren but rather the Master of Teachings Lord Shakyamuni of the Original Doctrine], should you persist in your mistaken belief, it then becomes impossible to maintain a pure faith by the principle of "two differing thoughts".
So yes, until you know the truth, you may continue to accrue merit and virtue (benefit) even with a mistaken belief or a mistaken object of worship but once you know the truth, if you persist in embracing a lie, your merits and virtue will wither and die.