Hmmmm.............I'm not sure that I'd get my hopes up just yet. Geographically its more likely that Saudi ATC would coordinate with Jordanian ATC, as they have done for years. And as the Jordanians appear to have more cordial relations with Israel, onward coordination with Tel Aviv would I suspect rely on Amman. Same in the opposite direction. I'm open to correction on that, but I don't think the radio work would be any more complex than the old "Confusion Corner" leaving Syrian airspace and entering Nicosia FIR and vice versa.
And looking at a chart, I don't think the time savings would exceed about 15 mins. Still a significant saving once schedules return to previous levels though.