Speaking in general, common sense dictates that any post traumatic stress disorder is going to have serious implications on the ability to exercise the priviliges of a class 1 medical certificate ( or indeed any class of medical certificate).
Traumatic events in an individuals life often have stressful repercussions that usually become less so over a period of time, this is not at all unusual. It does not always follow that such stress is classified as a disorder although for some people that is sometimes the case. The fact that the stress is classified as a disorder means that it does impact on an individuals everyday life.
In the event of an airline pilot holding a class 1 certificate and having been subject to a recent and serious traumatic event, the authority would be very likely to suspend the priviliges of the medical certificate, pending assesment by a psychiatrist appointed to the authority. It would presumably follow that the issuance of a certificate would also be subject to similar if not greater scrutiny.
PTSD or indeed many other temporary or permanent conditions are not to be taken likely. However common sense would also suggest that commercial aviation is not an acceptable therapy for such disorders and your friend may well find difficulties associated with an aviation career if the condition has been diagnosed and remains relevant. As you say the CAA would be the authority and their early advice would be well sought.