Your car insurance will state that you are not covered for racing or competitive rallies.
But you can go to a private race track and belt round (uninsured) if you want. Or drive cars owned by the track, on their insurance.
And your insuance company is not going to freak out and cancel your policy. You can still drive home.
I would expect the AMA insurance to work the same, unless it is run by some weird control-freaks.