Not wildly impossible I guess however would the F-14 fit into IAF doctrine & tactics. The reason I ask is that well when it came available the IDF did not go buy them.
They evaluated them, found them to be good planes but overkill for what they needed and wanted. Range was not an issue for Israelis and specially not for fighters. Extra punch with Phoenix missiles will not be worth extra cost and maintenance.
Also F-14 was pure fighter which means it would be replacement for Mirage III, which at that time were still relevant and fleet being improved by Mirage 5/Nesher. Those were known and proven quality, F-14 being still new much less so. And that holds true for Phoenix missile. Not to mention Israelis needed numbers and for same ammount of money they could get more Mirages than F-14s. And with former could depend on existing training and support infrastructure and established doctrine while latter would require building all that from scratch and figure out best ways to use them. And all that during War of Attrition.
F-14s advantages wouldn't be of much use during YKW. Arab air forces weren't as big a problem as SAM/AAA. So while F-14s could hang behind the front and fire Phonixes they would be burning big and expensive missiles for small targets. Though they could be airborne over central Israel and act as sort of reserve to quickly engage in either front when needed, Phoenix's great range allowing them to engage without need to approach frontline, so acting faster. And could be used to harass Soviet transport planes bringing supplies to Arabs far out to the sea.
So other than "cool plane with cool missile" there is little that would recomend F-14 to them and a lot that would make them say "thanks, but no thanks"