Firstly, I'd just like to say that in my opinion everyone should play through NieR: Automata at least once if they can as its an absolute masterpiece (and not just route A). I can't recommend it enough.
But to answer your question - the Nier raids are aesthetically and visually very representitive of NieR:A as most of the music is straight from Automata, save for the boss fight remixes, as someone else already pointed out. 2B's outfit is absolutely identical and I believe every piece of gear that you get from the raids is either taken from the game itself directly or from something related to Automata that isn't the game itself (but is still official Automata material). The Pods and Stubby minions are from the game as well.
Story-wise however - not in the slightest. The raids have locations that are visually similar/the same to places from Automata but the story is not in any way related to it. I won't go into Automata's story, I'd just say go play it and find out yourself instead. It's worth it.