I used to know someone involved in launch insurance. It's a thing. Presumably not one available to super secret squirrel launches like this, though (although one might guess that Northrop could sort something out).
Launch insurance can absolutely be given to classified payloads. My understanding of the launch insurance business is you say "my payload is worth $(X)XXX million to me and we're launching on this type of rocket" and the insurers look at the history of that rocket and your history as a payload manufacturer and charge you a 10-40% premium that gets built into the cost to the government.