I’m going to very hesitantly and with much caveats say no, they will not spam you, as long as you set your preferences to not send you emails, and unsubscribe from any they do send.
I have a normal Walmart account that I use to get curbside delivery of shampoo or whatever, and looking back through all of my emails from them, they are all directly related to orders and logging in. No ads or other junk. Additionally the order emails themselves don’t contain additional ads, beyond a standard footer with links to Walmart.
My conclusion is that Walmart in general is well behaved regarding unwanted email. I cannot guarantee their media division feels the same way. They might email you an ad every time you use the volume button, but that would be inconsistent with the behavior I’ve experienced from them.