I am not sure if you mean a caster trying to believe their own illusions or someone else's when they know they are illusions. Fortunately, this is General Discussion, not Rules, so my feelings on that are:
While there is wording or at least precedent for being able to fail a saving throw on purpose, I believe the wording for illusions (specifically for disbelieving them), is that if faced with proof, then it is automatic. If you are referring to the caster of the illusion trying to truly believe the illusion they just created is real, then I would have to say no. It would be like... doing something to yourself in private with your hand, but closing your eyes and pretending it were someone else doing that thing or some other act to you. You might have a really great imagination, but you know it's really you.
So unless you legitimately get amnesia or have a modify memory spell cast on you to make you completely forget that you created it, then it is not believably in-character to not know it's an illusion. And even if you did lose your memory, since it is in the nature of people to note and take stock of inconsistencies and problems with illusions that reveal they aren't real... if you interacted with it it wouldn't be believable for you to automatically fail it then either... since you wouldn't know you were trying to auto-fail your illusion.
This means a caster can't just create an illusion of a wall (not illusory wall, that has its own mechanics, though the caster can automatically see through that as well) to not see a medusa or basilisk on the other side, though it might help any allies.
As for someone else's illusion, I think it is probably allowed by the ruling. Technically someone telling you not to save against their illusion so you don't see through it adds an automatic +4 to the save, but I think despite that it can still be auto-failed. So if you're trying to entertain yourself with illusions, you need someone else to be in control of it.
Those are my thoughts on the discussion.
