It's certainly possible, but not under a classic car policy, which typically includes agreed value, limited mileage and use of another car as conditions. Many years ago I used to run classic cars as daily drivers (and my only car), but then I got sense......
Realistically, unless your use of a car is optional, they are not practical as an everyday driver. They will let you down. They may be off the road for weeks whilst waiting for parts when they do break down (note: "when" not "if"). Have you considered getting a cheap to own everyday car as backup and your "main" car in addition to the classic?