Can you cook with a glued clay pan?

Well, it all depends on whether the superglued section will come into contact with the food at any time. If you are going to superglue a handle to a pot, for example, it wouldn't harm the food but there are chances that it may fall off while you are carrying it.

If you wanted to be safe, you are better off not supergluing anything that will go near food or be used to prepare food.