Yes, moving your site to a different URL will break things. SSL keys are generated for a specific hostname, so you can't just ship the database to a new URL and have it work. Likewise, you had the problem with the wwwroot in the host table for your local host.
Moving wwwroot when using MNET is a tricky business because of these issues. You _certainly_ have to regenerate the SSL keys, and you _probably_ have to look around in the db and fix the wwwroot for the host idenitified by $CFG->mnet_localhost_id.
PeterB and I came up with a plan to ditch that particular row out of the host table, but neither of us have had time to implement it, or even file a bug for it I think. Though even if that was fixed, you'd still need to delete the keys when moving wwwroot, which I don't think is mentioned in the documentation when it should be.
BTW: the couldn't connect to host message is a http level thing, are you sure that you're trying to connect to the right host/port, that firewalling isn't in the way etc?