I don't believe that a pure neural network can currently abide by the rules of chess, even with unreasonable amounts of training. Do you have a counter example? I never mind having beliefs challenged with facts lol

edit: I think you could provide an AI with a service or skill that asks "is this move legal" but given all the overhead for llms or whatever to call a "legal move" service external to its process, well then you aren't really searching the tree very efficiently lol.

However if you just let a neural network score boards and the neural network is in the same process well then I think thats the working solution for using neural networks in chess. The net does not need to score all boards either, simple value based heuristics can obviously provide a preliminary list of good boards (moves) at a certain depth or ply and then select the move that produces the board that the neural net scores highest. I kinda sorta think thats whats done today but as usual I could be full of it lol