"More susceptible" is not the same as "susceptible". If it's bigger than an atom, we don't need to take quantum effects into account to get a good approximation, and moreover any effects that do happen are going to be very small and won't affect consciousness in a relevant way (since we don't experience random changes to consciousness from small effects). There's no need to accurately model the brain to perfect detail, just to roughly model it, which almost certainly does not involve quantum effects at all.

Incidentally, there's nothing special about quantum randomness. Why should consciousness be related to splitting worlds in a special way? Once you drop the observer-focused interpretations, there's nothing related between them. If the brain needs randomness there are easier sources.