I've heard that 18% gray cards are intended specifically to aid on determining the right exposure for photography, and only coincidentally for white balance. Is this true? Is it better to use a different type of aid for setting white balance?
Short answer, black is too dark to not clip reliably, white is too bright to not clip reliably. You need something that is pleasantly in the middle to give you an idea of proper curves and balance. A medium grey card is ideal for the purpose of determining the curves and the color of the lighting in the scene. The percentage is chosen for exposure, the color is chosen for the white balancing.
My understanding is that your camera attempts to expose the mid range of your photo to be 18% grey so these card are most useful for exposure. However an incident light meter will be a bit more effective.
Depending on your camera model you should be able to measure a scene and set a custom white balance based off off a reference photo. This reference photo can be of any neutral coloured thing from white to dark gray, or even better a colour chart, and does not need to be even in focus, so I doubt you specifically need a grey card for this purpose, however it would be useful. I think this would probably be the most effective way to set the white balance, although given that you could have multiple light sources at a different temperature even this is not fool proof.
To set a custom white balance on my D600 I use
PRE setting for white balance. For more information: