Yes. Thing is like this:
If everything’s correctly set (as it comes in the default state of the 1-click Droplet), unicorn.sh will be run when you do sudo systemctl start unicorn. When this happens, the environment variables you export in that script will be set and valid in the scope of that execution (this means the unicorn process). If you want to set others, for example to run bundle exec rails db:setup you can do it in the .bashrc file for the current user (e.g.: rails). By the way, doing that last thing is recommendable in my opinion, since adding RAILS_ENV=production after those kind of commands doesn’t work at least for me.

Hope this helps!