In the event of successful yom kipper with pre 6 day war borders demilitarized and joint sovereignty over east Jerusalem between Israel and Jordan
Yeah, that's definitely not happening. Mostly since Jordan wasn't involved in the Yom Kippur War (plus it's questionable that they even wanted the West Bank back). But also because the Arabs were definitely not after
status quo ante
But let's say that the Ramadan War is successful and, er, well, we don't need to focus on what happens, really, for the purposes of our discussion.
Would Sadat be able to use the prestige from a victory to successfully merge with Sudan,Libya and possibly Syria and Iraq
Definitely not Syria or Iraq (they're not falling for that one again - even with a land connection that, uh, definitely doesn't follow the Mediterranean coast north of Gaza city). Also definitely not Libya (what would Qaddafi possibly have to gain? And he's strong enough that the people aren't going to overthrow him to join Egypt) Sudan is the most doable, since their government is still pretty unstable and fragile, its president doesn't enjoy much popular support, and Egypt could draw on historical ties to justify it - though I'm honestly not sure how much the Sudanese were into pan-Arabism (or, frankly, if the Egyptians considered them "Arab enough").
What would be the impact on region with a successful union
Probably pretty minimal, honestly. A more powerful Egypt might be able to throw its weight around a little better and promote pan-Arabism, but honestly, it's still pretty rough. More boots in Yemen, for example, still might not
do anything. The Israel problem (if it's still around) needs structural changes to happen, not just more guns. Sudan, frankly, is completely destitute and will probably cost more in peacekeeping than it will generate in taxes and conscript soldiers. And, most importantly, the two OTL examples we have (UAR and Arab Federation) both fell apart very quickly.
Man, I feel like all I do is go around telling people how implausible their MidEast ideas are
EDIT:
Such would never happen, as the Israelis were willing to go nuclear to prevent such.
There's success and there's success and there's success (notably, OTL the Arab leaders called Yom Kippur a success, though God only knows how they spun that). There's definitely ways that the Arab forces can "defeat Israel" that don't involve Israel feeling scared for its existence, and even if it was, the more likely result is the US pushing the USSR to push the Arabs to halt. Israel is not and never was as nuke-happy as people seem to think. If nothing else, trust in enlightened self-interest, since any nukes going off in the Sinai, or, hell over Cairo and Damascus are going to be contaminating Israeli food and water for decades.