No, he doesn't. Due to the while() condition variable 'conductor' cannot be null when delete is called.
One problem with this code is you're calling delete on a pointer that you haven't checked to be NULL.
No he doesn't, deleting null pointers is safe.
You get a seg fault when you're at the last node in the list and calling delete on the next pointer which is NULL.
The real problem with this code is:
while(conductor != NULL)
temp_conductor = conductor->next; /* If temp_conductor becomes NULL... */
delete conductor; /* (delete works anyway) */
conductor = temp_conductor; /* conductor becomes NULL too... */
conductor = conductor->next; /* so 'conductor->next' = (null)->next = seg fault */