My 17 year old had a permit, we did
not add him to our policy for those few mos. When he passed the road test I went online and was unable to get an actual quote without giving all our info, so I plugged him in our policy on the oldest vehicle (crv/98) as the driver. Our policy went up 980. for the year. When I tried to remove him, I could not. He was automatically added, I called geico, was told that since we alerted them and he lives in the household (therefore all the vehicles are accessible to him they
must include him). Ouch...I was not too happy...but need him covered
BUT,
they then reviewed the policy and asked me if he used the vehicle everyday, and he does
not, uses it maybe on a weekend. I was told that he could be added on the policy but
NOT associated with a specific car at a much reduced rate. So thats what we did, the policy went up 200/year.

I was told that when he is 18 he can take the defensive class and get a reduction
or get his own policy. In the meantime he will not get "credit" as a good driver
until he has a policy in his own name.. so technically he could be 23 and if he never had a policy...then be charged $$$$ because he was not on own policy
As far as who is covered in your car as a driver, ANYONE that drives your car is covered under your policy for liability and no fault (NY) but that does not mean one should ignore purposely NOT adding a teen to a policy. A carrier CAN deny coverage (if they can prove) that an insured/policyholder intentionally did not add a person they knew drove the car or had full accessibility to it.
And an excess policy for a million, was much more reasonable than you would think.