Hi
Before answering this question, we need to understand first that what a mutation is. A mutation basically is a change in the DNA or genetic sequence of an organism that can significantly affect or not affect the function of a specific gene in organism.
Now coming towards the question, yes ofcourse it is possible that a Norwar rats population carries a different genetic mutation than a population os same rats in Africa or any other region, Why? Because sometimes environmental factors of a certain area can cause the population of a region to undergo mutation (For example harsh UV rays) and the other population donot contains that mutation. This will cause a slight change in the genetic makeup of the population of rats of Norther America. However, if the changes in genetic makeup continues to happen in North American Norway rats, a time will come when they will be genetically very different from same rats in Africa and in this way they will become a separate or different specie, this phenomenon is called speciation.
Hope it helps!