The October War is often wrongfully said to have been the closest the Arabs have come to securing at least a limited victory over Israel.
Fixed that for you. It should be the 1948 war, but nobody seems to take notice that it's the only war where an Arab army was able to obtain Israeli territory by force of arms.
This was partially due to the realistic Egyptian (though not Syrian) assessment of their capabilities and proper planning around this.
Wrong on both accounts. The Egyptians were right that they cannot defeat Israel if they try to retake the entire Sinai, so they developed the beliefe that trying to fight the same enemy, only limiting yourself to smaller gains would logicaly lead to better results. It didn't work out, as the Israeli crossing and circling of the third army proved. The planning was also lacking in so many aspects I can't realy figure where to start. There is a difference between a plan that looks nice and orderly on paper, where everyone down the chain of command down to the last soldier knows what to do at T+16h34m45s, and a plan that bloody works.
However, the tide turned against the Egyptians when Sadat first ordered a further advance into the Sinai,
No, it turned the second Egypt declared war, should have been visible by the sixth hour(ish) of the operation, and only dawned on Egypt around the 16th/17th of October.
which went against the Egyptian plan.
Again, false. It went exactly according to the plan, the only difference is that the plan said to go there if things look like you are winning, and based on several pre-conditions. Like I said, Egypt by this time still has no idea of what is realy going on, and assumes that so far all is (pretty much) good.
It is argued by some in the Egyptian high command that Sadat was one of the reasons that the Israelis were able to break through the Egyptian lines at the Battle of the Chinese Farm.
They don't say, these people who are responsible to plan and execute the plan blame Sadat, for an order he gave about a week after the setting for defeat was there, for thier failures? Shocking.
So the question is, what if Sadat decides not to interfere in the conduct of the war, and it results in the Egyptians staying put rather than launching another offensive? Do the Israelis manage to break through anyway? Is their task significantly more difficult?
Regarding Sadat it's hard to say, as there are different depictions of just what were Egypt's goals. So I'll just stick to the usual "WI: No Egyptian offensive on the 14th?"
No, the task is not significantly more difficult.
The Time: The plan to cross was originally intended for the 15th. Intelligence that an Egyptian offensive was planned for the 14th meant that there were a few movements of units to defend against the coming attack, and then on the 15th some movements back to the starting points for the crossing on the 15th. So as far as the time factor is concerned, we are still good to go.
The Location: The seam between the Egyptian armies was known since about the second/third day of the war (can't recall right now, I'll check if anyone wants), when a full Israeli recon battalion went there to spend the night and make sure there are no Egyptian units there. There weren't, since like I said a few moments ago, Egypt lost the war on the first day. The plan was to start off with 5 divisional beach-heads with a 10km radius, that will later link up and creat the first stage of Operation Badr, a 10km deep defensive line, from which the second stage (the one we are discussing) will be launched from,, together with the copying of the missile wall to the eastern bank of the Suez. Now Egypt lost the war when it failed to fulfill stage 1, and later still tried to fulfill stage 2. The Seam was not only across the entire Great bitter lake, but it also streached a bit to it's north, thus creating an opening for Israeli forces to begin the crossing, before Egypt knew that anything was going on. So as far as the location factor is concerned, we are still good to go.
The Opposition: During the offensive on the 14th, Egypt lost over 250 tanks. Now this is the point where usually people think that Egypt could have profited from not launching the offensive. "If Egypt holds on the 14th, it still has 250 tanks and more guys to hold the Israelis, right?". Not exactly. See, these 250 tanks were lost all along the front, not just from units close to the crossing point. Those were around 20 or so. Not a big deal, especially when you consider that the problem was not with the numbers, it was the command. The Egyptian forces from the 2nd army couldn't hold back the Israeli forces due to problems with synchronizing the defense properly. The whole allignment was set to defend to the east, not to the south. The forces from the 3rd army, well, anyone who has a little understanding of what happened to the Egyptian 25th armored brigade, and why that happened, understands that numbers mattered little there, and that simply saying "well, here is another 100 tanks" just isn't good enough. So as far as the opposition factor is concerned, we are still good to go.
So to repeat my answear, no, the task is not significantly more difficult.