OnStar IS Verizon in most of the US, Bell Mobility in Canada. They may fill in the gaps by roaming onto other CDMA networks.
OnStar Phone VS Verizon, in the US you are simply choosing to pay General Motors for Verizon voice service.
OnStar Phone thus cannot work where there is no cell service. However the phone in the car might work better than the phone in you hand, because its antenna is outside, not shielded by the metal shell of the vehicle.
If true that GM is switching carriers from Verizon to Sprint, expect bigger coverage gaps, depending on roaming arrangements.