Strategically the answer is no because the third army was resisting against the idf and they still fought them till new ceasefire in Jan 1974. The last martyr of this war died in 14 Jan 1974 and he was in the third army. The IDF was also encircled in Egypt also because the army weren't that big but rather small and Egypt was preparing a counter offensive to those forces who crossed the Canal. First they lost in every big cities like Ismailia battle by Ariel Sharon and Suez battle (the last battle of the war) by Adan. They intended to cut the supplies of the 2nd and 3rd army and they failed. The counter offensive was called Operation Shamel
https://ar-m-wikipedia-org.translate.goog/wiki/الخطة_شامل?_x_tr_sl=ar&_x_tr_tl=en&_x_tr_hl=en&_x_tr_pto=wapp
Egypt did exactly what Israel did also. Moshe Dayan wanted use their nuclear bomb and Golda Meir and other generals refused this idea (in the beginning of the war).
@Gomig-21 @The SC can explain in details more about this operation.
But first we must continue and the thread and not ruined it. We can open a new thread about the third army etc... But let's focus in this thread.