Will your uninsured motorist coverage cover an accident from an at fault unlicensed uninsured driver?

Yes. The initial trigger for entitlement to uninsured motorist benefits is involvement and injury in a motor vehicle collision with an uninsured motorist. According to state law, there may be other requirements as well (such as the existence of a permanent injury or significant scarring), but lack of insurance by the adverse party is the first requirement.

Note also that, again depending upon state law, if you as the injured party negligently caused or contributed to the collision, your recovery may be reduced accordingly.