That would depend on whether he actively considers it as something to rely on, as opposed to an assumption so baked in he forgets to question it, right? If questioned I think Quirrell would rightfully consider the Chamber to be something critical enough to be worth having other contingencies for, but he just never considered it necessary.
For me that fell under ‘My simulation of Voldemort isn’t buying that he can rely on this, not for something so crucial.’
That would depend on whether he actively considers it as something to rely on, as opposed to an assumption so baked in he forgets to question it, right? If questioned I think Quirrell would rightfully consider the Chamber to be something critical enough to be worth having other contingencies for, but he just never considered it necessary.
And the basilisk is already dead, so there’s nothing useful to find there anyway.