can a 15' touring kayak go through class III rapids safely?

Depends...does it have a rudder? I would do it only if you have a lot of expereince in both (the boat and rapids..).

CLASS III

Rapids with moderate, irregular waves which may be difficult to avoid and which can swamp an open canoe. Complex maneuvers in fast current and good boat control are often required; large waves or strainers may be present but are easily avoided. Strong eddies and powerful currents can be found, particularly on large-volume rivers. Scouting is advisable for inexperienced parties. Injuries while swimming are rare; self-rescue is usually easy but group assistance may be required to avoid long swims. BOC note: We recommend swimming ability for class III rivers and up.

I would say most likely not. I'm sure that a professional could probably find a way to navigate anything, including class III rapids, but that is a really long kayak to be managing through rough water, and I'm not sure how long anyone other than a professional could go before getting the kayak severely damaged.