You can't feed video to a monitor without a graphics card, as far as I know. That being said, most motherboards these days have integrated graphics on the motherboard. If your motherboard has integrated graphics, then yes, it can run without an external graphics card in it.
Laptop: Dell XPS 17 | i5-2450M @ 2.5GHz | 6144MB RAM | GeForce GT 550M
Desktop: HAF 932 Advanced | i5-3750k @ 4.4GHz | CORSAIR H100 | ASUS P8Z77-V | EVGA GTX 680 2GB | 8GB G.SKILL DDR3 @ 1600 | MUSHKIN 240GB SSD | WD 500GB 7200RPM HDD