had same question some time ago
It depends on why you want to manage chef server by Chef, because
chef-server-ctl reconfigure uses chef-zero for server configuring and recipes are not convergent, they idempotent (Chef doing changes each run).
My proposal, don’t be dependent on Chef server, act like you can lost it any time. Keep your cookbooks and environments in Git and/or Supermarket, make backups of following files:
With this files you can start new chef server with same configs, secrets, etc. so integration with application (Analytics, Supermarket etc.) will be kept.
cheffish (https://github.com/chef/cheffish) resources you can manage organizations, users, keys etc. on your server.