No they won't do that. The AGREED VALUE is the value you have already agreed with the insurance company when u signed up for the policy. It doesn't matter what the price of the car you bought it for, as long as it is around the same range as the agreed value, you should be fine.
A friend of mine wrote off his S15 a while ago. He put an agreed value of $32,000 with JustCar, the price of the S15 was only about $29,000. He got back $32,000 minus the premium of his policy.