I have done something very similar. I have a new Discourse instance live at subdomain-new.example.com, but with subdomain.example.com in the app.yml. Anecdotally, the domain setting seems to affect redirects after SSO, i.e. if I click “Log In” I am put back on the old Discourse instance.
I am still able to verify that the data and settings transferred to the new Discourse instance, which I think was your primary concern, and it doesn’t affect my existing Discourse instance at all.
As an aside, I think it might be worth explicitly stating in this HOWTO that after a backup is restored, the new Discourse instance should be rebuilt - I skipped over this step at first and didn’t find the existing language about “enabling any optional configuration settings” to be clarifying. Once I thought through how Discourse operates and rebuilt the app, all the settings, themes, custom images, etc worked perfectly.