Classical computers also do things "at the quantum level"; CPU gates rely on quantum effects, probably the HDD does too, etc. But it doesn't prevent understanding because that computer part implements a simpler interface.
The brain probably isn't a quantum computer, or else we'd be able to factor integers quickly in our heads.
According to philosopher Paavo Pylkkänen, Bohm's suggestion of the quantum mind "leads naturally to the assumption that the physical correlate of the logical thinking process is at the classically describable level of the brain, while the basic thinking process is at the quantum-theoretically describable level". [1]
Factoring integers is a logic operation (thus not performed at the quantum level). But an operation like identifying an object or a smell (as it is what the article here is about) could be performed at a more deep level using quantum mechanics.
Hmm… it seems like that's only true if it doesn't actually mean anything impressive. Your neurons or nose obviously can rely on quantum effects in the same way a modern semiconductor transistor process does. But that doesn't imply anything huge like "consciousness can't be emulated on a classical computer."
The brain probably isn't a quantum computer, or else we'd be able to factor integers quickly in our heads.