Poirot's mind raced back over the details of
Achille Poirot's career. Had all that really happened?
"Only for a short space of time,"
Since the "Achille" that appears in "The big four" is grown-up, if he were a real person he could not have been Hercule's brother "For a short space of time". The inference is that he was imagined for a short space of time.