I don't think so: the human mind doesn't run on a Von Neumann architecture, so any speed/search depth tradeoffs wouldn't behave in a computer-like way and a lot of other intuitions about computational performance don't apply. All else being equal, uniformly slowing down the human brain's operations probably wouldn't impair its ability to exhibit behaviors we'd recognize as conscious; they'd merely increase the time it takes to get an output given some input. Most importantly, human-unique capabilities like language would probably be left more or less intact (if slowed down).

A lot of animals actually have significantly faster nerve conduction than humans, although I don't know if this extends to the brain.