If a graphics card has a six-pin PCI-ex connector, you can better connect the six-pin connector. As long as the connector is not there, the graphics card will draw that power from the motherboard, possibly overloading the PCI-ex connector and damaging the motherboard.
It can also destabilize the system by either the graphics card not getting enough power and crashing or drawing more power from the motherboard and destabilizing the power supply to other motherboard components, which they will crash, causing a blue screen of death.