No. As a rule it's nothing to do with your GP and they are not contacted.
The exception is if you have a pre-existing medical condition for which the AME/CAA require more detailed background information. For example, I fractured 2 vertabrae in my back in a motorcycle accident years ago which I was honest about on the form. They wouldn't issue my medical until they'd had confirmation of the nature of the injury and treatment from my GP.