There is no link between the two.. In other words, there is no existence dependency of a video card to a processor or vice versa.. The processor to work requires a compatible socket and the video card to work requires a compatible slot.. Of course both require the correct power..
Sorry for the above post^
The Core 2 Duo is the chip that you are talking about. The Core 2 architechture comes in a couple of flavors - Core 2 Duo (dual core) and the Core 2 Quad (quad core)
Just as Emperus has stated the CPU doesnt really matter as long as the motherboard has the correct slot/interface for that video card (quadro 1800)
With this in mind you should be able to use it with no problem. Now with that being said, the only problem may be that the CPU that you use may not be powerful enough to really feed the video card with data for processesing. If Core 2 architecture is what you are going to use make sure that it is at least an E7xxx chip or better.
Now my questions are ----- Why a Quadro? Are you doing with it - graphic design, 3d autocad work, gaming or what. Knowing what the use of the card will be will help to give good advice on it.