There is always that "inside the story" versus the "outside the story" angle, isn't there? From inside, it's Bilbo's tale, "There and Back Again, a Hobbit's Holiday," which is a far cry from the same viewpoint as a person on the outside, reading the story as part of a much, much bigger and greater whole. As presented in the Hobbit, just about everything has the feeling of being less than it is in LotR and TS. The Elves of Rivendell are silly, the Dwarves might well have been given names like Grumpy and Fatso, the Elves of Mirkwood are party guys who get nasty and bigoted (possibly from party hangovers), the terrifying trolls are the Three Stooges.... I'd say there's a lot of Bilbo's naļveté in the depictions of peoples and places we see in The Hobbit (now, who really believes that Gandalf's eyebrows stick out beyond the brim of his hat?
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That said, IF Gandalf had died at that juncture, I suspect that several matters would have led to his return, but probably not as the White at this point (the fact that Bilbo notes that Gandalf seems to come and go without notice or warning could set up a scenario in which, having been left behind, presumably dead, when he shows up later as his usual self, it would be supposed that he had not actually died but had again gone off suddenly, or merely appeared to be dead, "playing possum" for the benefit of the goblins). If Eru knows all that is going on in the world, He would know that Saruman is already heading down the wrong path, but may yet turn back, with help and support. Gandalf is likely the only person who could give it to him, as Saruman's pride would not accept it from lesser beings (Radagast included; he never appeared to have anything but contempt for him). There is no need for Gandalf to come back as the White at this point; in fact, it could cause a lot of problems, and serve to further separate the peoples the Istari were sent to unite, as it would undoubtedly put a huge rift between Gandalf and Saruman and almost ensure that Saruman would side with Sauron. Coming back as the Grey, yes; there is a considerable amount of work left for him to do, especially in guiding and protecting Bilbo, who was meant to find the Ring, and Frodo, who was meant to carry it to Mordor. And there is still that Balrog potentially waiting in the future, where Gandalf can die again, and THEN come back as the White.
His death now, just as the Ring is coming out of hiding, would be bad, and I could see that Eru would not want Gandalf taken out of the picture just yet. However, I think that if Eru were to take a hand in this (presuming Gandalf did hurl himself down from that tree), it would be to make sure he did NOT die. Landing on a group of suddenly conveniently placed goblins or wolves could be enough to do the trick. He might come out a bit injured, to cover up the "miracle" -- but then, being a wizard, if something miraculous HAD happened, others might just put it down to being a wizardly trick.
Interesting thought, though.