I am going to be honest, I don't recall off the top of my head, but it is getting passed in as an argument to the other modules above so I assume so. I was able to verify that the other two were getting exported by adding a null resource that was something like:

    resource "null_resource" "echo" {
      local-exec = "echo '${module.root_mws.account_id}' > output.txt"
    }