Nej, I bet they have some sort of algorithm which distinguishes your home IP restarts and totally different locations. I've restarted or just flat out lost my internet connection numerous times and I never got auth banned, and my IP just like yours changes every router restart.
Assuming you would however have to contact admins every router restart, it wouldn't be that much of a pain in the ass. The support is online pretty much all the time and they respond rather quickly, so that wouldn't really be a problem.