This may be a lot of explaining for a very simple question and a very simple answer.
I've been creating websites at a dev location on my server, and then moving the WordPress installation over to the final location when all is approved. For example, I would create the WP site at http://dev.mywebsite.com/client_name/ and then move it to client_domain.com when it was all approved. The directions are well documented at http://codex.wordpress.org/Moving_WordPress.
Good, but I often have the situation where the client's current website is either non-existant or hosted on another server, so technically I can create a new WP website at its final server location (as an add-on domain) and not have to go through the hassle of moving it. The issue is that what will eventually be a WP site located at future-client-domain.com can be actively worked on by going to future-client-domain.mywebsite.com, so that's how it's set up. The WP site will work but it's set to this subdomain and not the direct domain name.
So my long-winded questions is this... will this be as easy as changing the "WordPress Address (URL)" and "Site Address (URL)" settings under General Settings? Would that stupidly easy tweak fix the site so that it will totally work though the client's domain name once that gets transferred over? It seems like it shouldn't be that easy but perhaps it is. And I didn't want to go down this long production path only to have to do a possible double-move if it turns out I was wrong.