Israel tried that in the period thy held the Sinai, establishing settlements there and partial annexation was actually discussed IIRC. They decided that doing that (meaning continued conflict with Egypt and the costly maintenance of a revamped Bar-Lev line on top of all other commitments) was no really worth it. It was controversial but very sensible in removing a powerful player from the already very long list of sworn enemies.
This would probably stop cold any Egyptian approach to the Western Bloc, keeping them pretty firmly Moscow-leaning, unless, of course, the Americans don't decide that Israel wants too much and is not a reliable ally; this, in turn, is most undesirable to Tel Aviv, which would be isolated and in worse overall strategic position, havig to deal with Egypt, Syria, the PLO. Invasion of Lebanon is probably not happening here, but conflict in Galilee will still occur.
I doubt Israel is going to do an alternate Camp David with Syria (returning the Golan Heights) which would make them quite overstreched. Arabism is a stronger ideology for longer (as oposed to Islamism) as Sadat's policies would be very different in this world.
The Lebanese civil war will probably still occur and be even more of a confused mess.
Hmmm... I doubt it would really be sustainable. Unlikely, and too many variables.