You should not have any problem. You just need to tell the insurance company you have a finished basment.or you don't tell them then the basement will not be covered, but it should save you few dollars. They never asked the permit.
When you purchased the house, the "title insurance" will cover the permit issue. When you did the house inspection, the inspector should have checked the wiring and so in the basement.
Then you just need to let the insurance company knows you have a finished basement.