From what I can see above, I think you should be fine. The Kentico BD does not contain any DNS settings. There could be custom work that I’m not going to be aware of and that does add some risk.
If your developer has changed the location that files are stored, then this may also cause an issue. There is a table called CMS_SettingsKeys that would contain these setting if that has been done.
I’m assuming the website domain is the same on both sites, but if not you may need to look at the Sites application, and maybe licenses too:
I can’t think of anything else off the top of my head. If you can contact your developer though to double check, I’d recommend doing that. I know I’d rather get a call about something like this that potentially have to come back after a holiday to fix any issues.