Late to the party, but yes, Egyptians are Arabs. As Greg M points out there are surely a few (Copts or who knows what) that will claim (accurately, for all I know) not to be Arab, but the great majority of Egyptians are Arabs. In fact, Gamel Abdel Nasser, the second president of Egypt, was a (if not THE) prime force behind pan-Arab nationalism.
And I can tell you most assuredly that the inhabitants of the Maghreb nations extending west from Egypt - Libya, Tunisia, Algeria and Morocco, certainly consider themselves Arab.