Yeah, don't do that. Like most things insurance, "getting insurance" i.e. paying the premium can be the easy part. But deep in your policy will be something about unpermitted work. And what you want insurance for is to be able to make a claim.
As a contractor, I have no love for Permits and Inspections mostly because is provides no assurance to anybody about a standard of work and the government's style is weak sauce. But I have little to gain from not pulling permits.
So there are many ways you can get "caught". It doesn't mean you will. So do you feel lucky?
A. Builders Risk Insurance - you want this and often a permit is part of the application
B. County Assessor - So you are supposed to pay taxes on the increased sq/ft., value of your property. The permit kicks off this process. If you go to sell, the title work, MLS and so will kick out redflag if it doesn't match. Now you have a unpermitted addition and you own back taxes.
C. Nosy Neighbor/ Inspector Drive By
D. Oh and the Contractor - Your guys suck, you owe him money, he calls you in. This about why a contractor would knowingly not pull a required permit? What's in it for him?
Your risk is probably a function of the situation. Is it a 10x10 mudroom out on 40acres or pop top visible from the street?
Short Story: Don't. What is the permit cost, 5% of the project?