Of course, it is widely held that, at the end of the war, IDF was in a position to conquer Amman, Cairo and Damascus with some effort. However, IDF had mercy on these Arabs and acceded to ceasefire after US urged so. Had it so wished, the map of middle east would be quite different today. All Arabs were indeed tamed at that war.
In the most extreme case, yes they could have but I don't think that the world would had sat back and watch three nations become apart of an Israeli land grab. Secondly, the IDF would had lost more soldiers and equipment during occupation of these areas and with the hate that exist with other Arab nations. I see the Saudis, Libyans, Algerians, and Sudanese sending more than their share of aid to those nations if that were to take place.
And if they where tamed, there would have never been a October War or a War of Attrition?
If you use that logic, you are simply covering up the incompetence of Arab armies, while at the same time, downplaying the achievements of IDF.