Tesla Coils - Is there a risk that the discharge can create x-rays?

Generally Tesla coild are fairly safe from the point of view of X-ray generation. You could potentially test for it using a sealed can of camera film with a high ISO rating, placing it in the vicinity of the coil while it is operating, and then developing it to see if it is fogged.

However, a bigger problem might be ultraviolet light, ozone and nitrogen oxides produced by the discharge. None are good for your health, but you can smell the latter. An article on safety here