No, that almost certainly wouldn't happen. If you declare, you're basically given cart blanche provided you can reasonably justify your actions, and if an AFB is closer than a civilian airport, for example, its absolutely okay to land there (though you should probably give them a call first saying you're landing). Your first priority is not dying; legal consequences don't matter when you're in that situation, and the FAA knows that. If breaking a law will save you they'd rather you do that than die, and they almost certainly won't punish you for it.

I'm not aware of any more serious consequence having ever happened for a legit emergency, and I am aware of fatal accidents where private pilots were e.g. out of fuel and didn't realize the AFB was an option even though they could've made it.