Theoretically, digitizing brain activity is definitely possible, and in some ways, has been done. A neuron only has two states; it's either firing, or it's not. That seems obvious, but what I mean is that an action potential, the electrical signal that neurons use to send messages, signal other neurons, and make stuff happen, is always the same.
It looks like this. Always. The two little humps next to the arrow represent getting a little bit of a signal, but not enough to cause the neuron to fire. If a neuron gets enough of a signal, it will fire, every time, and the signal it sends will always have the same strength, size, and shape; the only thing that really changes is how fast it goes through this process. Because of this, it would be easy to digitize a brain signal, because it's already binary. For every neuron, a 0 means it's not firing, and a 1 means it is.
But that's only digitizing what's currently happening. In order for digital reincanation to be viable, we can't just record what is happening, though. If we want the recreation to have our memories and personality, we have to be able to have some digital record of the signals the brain has sent in the past. Not just that, but for digital immortality, we need to have some way for the digital brain to respond to new situations with the same pattern of firing that original us would have. It has to be able to learn new things and recognize future patterns. It can't just be a digital record- it ALSO has to be able to act relatively independently moving forward.
Every brain digitization plan is well aware that we can't do that yet, and it will be a while before we can. There are too many outstanding questions that we don't currently understand. For one thing, in order for this recreated brain to be "you", it has to have your memories, be able to access and act on them, and make new ones. The problem is that we don't really know how our brains store memories. Memory is way too big of a subject to cover everything we know about it as part of this post, but some general things we know. We know that there are different kinds of memory, and something that affects one type may not affect another kind, so they must have at least somewhat different mechanisms. We know areas of the brain that are important for memory. We know that synapses, the places where neurons communicate, are important. But, most importantly for this, we don't know what a memory looks like in the brain, or exactly how to trigger a specific memory. That seems kind of important if you want your brain, and presumably your consciousness, to live forever; if we don't understand what a memory really is, how can we know that we're preserving the right information to recreate them?
And we are more than just our memories. Presumably, if you want to live forever, you want your recreated brain to respond to situations like current you would. You want that future brain to feel like you. We have no idea how things like personality and intelligence and other individual differences are coded in the brain, much less the beginning of an inkling of how to recreate them. As with memory, we have no way of knowing if preservation techniques are preserving the right things to make a future brain really be us.
A map of the human connectome
The cornerstone of Nectome's business is their brain preservation technique. This is what they've been getting grants and winning prizes for, not really for anything directly having to do with brain digitization. The idea is that their method of brain preservation works at an extremely fine level, preserving each and every synapse in the brain, to create a map of all of the connections, also called the "connectome". This is totally true. They've done this with a pig brain (fitting given the whole eating ham to celebrate a resurrection thing), and it is really freaking cool. The adult human brain has an estimated 100 billion neurons and 1 TRILLION synapses, and this process essentially perfectly preserves all of them. That is amazing. But....it also may be completely useless when it comes to digitizing brains.
Just because you perfectly preserve the structure of the brain doesn't mean that you're preserving the function. For one thing, there's a lot more that matters than just the structure of synapses: the presence and concentration of proteins, whether that synapse sends "fire more" or "fire less" messages, and what neurotransmitters are doing, just for a start. About ten years ago, researchers were able to fully describe the connectome of a nematode called C. elegans, and despite being able to recreate it, we still have no idea how it stores memories or a lot of other information. There's also the question of functional connectivity, the idea that areas of the brain influence each other when doing a specific task, but not necessarily all tasks. What tasks those are and why those areas move together isn't captured just by having a connectomic map. Simply being able to make detailed pictures of the synapses doesn't mean we can recreate the information the communicate. It only captures the structural state of the brain in a single moment in time, and that's....pretty useless, honestly.
Given what we currently know about the brain, there are a lot more questions that need to be answered about how information is stored and what in the brain makes us us before we can even begin to think about digital reincarnation. However, given what we currently know about the brain, it seems basically impossible that a physically preserved brain, no matter how well preserved, is going to carry even close to enough of that information to be able to digitally reincarnate us. That's not even to touch on the philosophical questions of whether a copy of your brain is really you and whether all we are is just learning algorithms. Nectome has a really amazing process that is going to be useful for a lot of things, but making us live forever just isn't one of them.