Basically, I plan to install Windows Server 2008 R2 x64 on a machine by plugging in the video card initially and then I plan to remove it completely because I need the slot for something else. The motherboard has no integrated graphics. Would I be able to RDP once I remove the video card even though the motherboard has no integrated graphics?
As long as the system is turned on and connected to the network, configured properly, etc. then yes, you can. This is how server administrators access "headless" servers
One note though: many BIOSes refuse to boot without graphics. Check your BIOS first, or else you may be head-banging the keyboard. If you have a PC SPEAKER connected to the motherboard (not a speaker system), then it should sound 1 beep if all is well