Short answer: No, changing the WB does not affect the RAW image.
But you don't need a gray card to shoot RAW and get a WB; the camera can provide you with an auto WB, or you can select one prior to your shoot, either through a gray card or through a camera preset.
So here's a tricky WB situation: you're shooting in a church with different naves. One has a gold chalice that the light from a stained glass window is hitting and bouncing everywhere, and everything looks pretty cool. Back and the main altar, you've got light from all over, maybe from incandescent lights above. You're moving back and forth between shrines during the wedding/baptism/whatever. Switching WB might be very tricky to do on the fly, and fraught with the possibility of a mistake. For this, I'd shoot the gray card in both areas ahead of time (if possible, if the light isn't changing much) and then apply the appropriate white balance setting to your raw file later.
In practice, I almost never use a gray card, and several of the other wedding photogs I have worked with have also ditched their gray cards as well. The Auto WB setting in the Canon and Nikon bodies is good enough, and the light changes so quickly, that shooting in RAW and then fixing the rare mistakes made by the auto wb is easier and faster than using the gray card.