I got a ticket in Norway for going 6 mph over the speed limit. If I pay the ticket, will Norway report the violation to my insurance carrier or to the Department of Motor Vehicles in my home state of GA, USA?
Out of state speeding tickets certainly follow you home, but countries don't share details - in many cases it'd be too difficult, as your rental car for example might have the ticket, and your rental company sends you a bill but the country charges the rental company.
The most likely risk is that your insurance might ask "have you had a speeding ticket issued anywhere in the last x years" and depending on the wording, you might have to own up.
Also note, if you're considering not paying the fine, some countries will chase you across borders, as described in this answer.
More reading in this answer I wrote a while back, about the possible expansion of a national US database to sharing with other countries.