According to Attention is all you need paper: Additive attention (The classic attention use in RNN by Bahdanau) computes the compatibility function using a feed-forward network with a single hidden layer. While the two are similar in theoretical complexity, ...

Indeed, we can see

Figure 1: Attention mechanism diagram from [2].

Thus, the alignment scores are calculated by adding the outputs of the decoder hidden state to the encoder outputs. So the additive attention is not a RNN cell.

References

[1] Bahdanau, D., Cho, K. and Bengio, Y., 2014. Neural machine translation by jointly learning to align and translate. arXiv preprint arXiv:1409.0473.

[2] Arbel, N., 2019. Attention in RNNs. Medium blog post.