The code contains two built-in pitfalls. First one, if it executes in a member function for an static, extern or automatic object, the program will possibly crash as soon as the delete statement executes. There is not any portable way for an object to tell that it was instantiated on the heap, thus the class cannot assert that its object is correctly instantiated. Second one, while an object commits suicide this way, using program may not know about its demise. So far as the instantiating program is concerned, the object remains in scope & continues to exist although the object did itself in. Usually Subsequent dereferencing of the pointer can & does lead to disaster.
You must never do this. As compiler does not know whether object was allocated onto the stack or on the heap, "delete this" could cause a tragedy.