Below are what the help page says about adding or changing a custom domain. In other words, it should just work. But if something should go wrong after migration, I would be surprised if @manton didn’t help out a paying customer and fix the problem. I imagine broken blogs are pretty bad for business in the long run. 
As well as adding a custom domain from
username.micro.blogtoyourdomain.com, you can change toyourotherdomain.comin the future. When adding a custom domain for the first time, or changing to a new one, various things may appear broken for a while:
- None of your images will load
- HTTPS won’t initially be enabled, so visiting your site may show an “insecure message”
Both of these are normal. Behind the scenes, we’re automatically setting everything up. Things should clear up in about 48 hours.