Yes, this is possible. The tattoo needle doesn't go deep enough to do any damage to your veins, no matter what state they are in. However, you may have to tattoo the area with somewhat dark inks so that the veins don't show through. Or you can create a design, with the help of your tattoo artist, that incorporates the veins!
You also have the option of removing the varicose veins before you get a tattoo. This can be a simple and fairly painless procedure. Whether you remove the veins or not, it might be a good idea to consult with a doctor before you make the decision to tattoo the area.