There is no question that a neuron uses a large fraction of its atoms for its functionality, as is every other cell. What I think you're postulating is that these atoms form a functionally uber-complex network with mind-boggling combinatorics - but that position does not align well with current science. Single neurons are not that smart. For starters, they don't have the I/O address space or bandwidth to be, nor do they have the energy budget to behave like a block of Computronium.
Neurons have not been opaque black boxes to us for a long time now. We understand a lot of the biochemical processes going on in there. We may not have a complete picture in many areas regarding many neuron types, but there is not enough unexplored space in there to allow for a cell-sized quantum supercomputer or anything like that.
The upper bound on a neuron's computational complexity is dictated by the intricacies of its protein machinery, which is many many orders of magnitude lower than the number of atoms making up the whole.