Hmm: NNUE was introduced in 2018, the AlphaZero preprint 2017, AlphaGo 2015-2016. I checked this because my memory claimed that it was AlphaGo's success that sparked the new level of interest in NN evaluation.
Wouldn't surprise me if AlphaZero's improvements had no influence in that timeline, but for AlphaGo it would.
The original NNUE paper cites AlphaZero[0]. The architectures are different because NNUE is optimized for CPUs and uses integer quantization and a much smaller network. I don't think one could credibly claim that it would have come about if not for Google making so much noise about their neural network efforts in Go, Chess and Shogi.
Wouldn't surprise me if AlphaZero's improvements had no influence in that timeline, but for AlphaGo it would.