Do any serious theories on the brain being predominantly digital hold any water with neuroscientists? I feel like it's fairly well accepted that the brain isn't digital even just with what we do understand about neurons?
The process by how the neuron determines whether it's time to fire or not is almost grotesquely analog, in that it is effected by a million different things in addition to incoming spikes.
How much of each process matters for what is the mind-generating part of the brain's work? We don't know.
Myelination (which allows very fast, and digital, communication between neurons) is universal in vertebrates, which points to it being important for intelligence.
As a counterexample, we have cephalopods, which accomplish their impressive cognitive tasks using only 'slow' neurons; they get around the speed limit by having huge axons, which reduce internal resistance. So we know that digital transmission isn't necessary for intelligence, either.
The nature of cognition is a fascinating subject, isn't it!
If you looked at the operation of a digital computer, you'd find an analog substrate, with some quite interesting properties. Deciding whether the analog substrate is an important semantic element of how the computer worked, or whether its operation should be understand digitally, is as much a (research-driving) leap of faith as anything else.