No they don't.
When we first applied, they refused and asked the agent to look at the odometer of my convertible. A year later, we reapplied and showed the car to the agent a second time and he noted that we had only driven it about 1500 miles. Since then, we've had no problem adding cars and we've never had to demonstrate our mileage since that time.
I would assume that, if I had an accident, they would want the current mileage and would calculate how many miles I had averaged a year since the policy went into effect.