This doesn’t work out of the box, I guess. You will have to set up the respective reverse proxy configurations and will have to set up multiple SSL certificates in order to support more than just one domain. Also a lot of plugins (especially the calls plugin) does also only support to specify one entry point for the call streams, so I think such a configuration is generally not really supported by Mattermost at all and the latest change to the desktop app just reminds us about that.
I think working with internal DNS overrides then or some kind of u-turn NAT is what should be done here, at the end of the day, it’s also easier for the sysadmin not having to ask where the user is coming from and to be sure that everyone is accessing the server using the same domain and the same route.
In a default, secure Mattermost setup, this should not be possible at all, given the fact that there should be SSL and HSTS enabled. Whenever you try to access the IP address directly, you would get an error message and the client would not connect anyways.
For connection debugging purposes, you can always send them via the webbrowser to your Mattermost domain and with regards to further troubleshooting options I’ve read that there will be a feature in one of the next desktop app versions to run some connection diagnostics directly inside the app, which might also help with situations like these.
The SiteUrl is also being used for several other things, like links in e-mails, OAuth integrations, etc., so while accessing the Mattermost server with basic functionality itself might work when using the IP address or alternative domain names, the best practice is to use just one SiteURL and make sure all your clients access the server using the same name:
https://docs.mattermost.com/configure/web-server-configuration-settings.html#site-url