Não. Na verdade, foi a ascensão de Sauron que levou Gandalf a encontrar uma maneira de retomar Erebor e remover Smaug do possível uso de Sauron.
SDA, Apêndice A Anais dos Reis e Governantes :
But at last there came about by chance a meeting between Gandalf and Thorin that changed all the fortunes of the House of Durin, and led to other and greater ends beside. On a time Thorin, returning west from a journey, stayed at Bree for the night. There Gandalf was also. He was on his way to the Shire, which he had not visited for some twenty years. He was weary, and thought to rest there for a while.
Among many cares he was troubled in mind by the perilous state of the North; because he knew then already that Sauron was plotting war, and intended, as soon as he felt strong enough, to attack Rivendell. But to resist any attempt from the East to regain the lands of Angmar and the northern passes in the mountains there were now only the Dwarves of the Iron Hills. And beyond them lay the desolation of the Dragon. The Dragon Sauron might use with terrible effect. How then could the end of Smaug be achieved?
Se Bilbo tivesse ficado em casa é provável que o Anel tenha sido encontrado por algum Orc:
SDA, Livro I, cap. 2 A Sombra do Passado :
The Ring was trying to get back to its master. It had slipped from Isildur’s hand and betrayed him; then when a chance came it caught poor Déagol, and he was murdered; and after that Gollum, and it had devoured him. It could make no further use of him: he was too small andmean; and as long as it stayed with him he would never leave his deep pool again. So now, when its master was awake once more and sending out his dark thought from Mirkwood, it abandoned Gollum. Only to be picked up by the most unlikely person imaginable: Bilbo from the Shire!
Sauron já estava se levantando bem antes de Gandalf se juntar a Thorin. E o Anel abandonou Gollum algum tempo antes que Bilbo o encontrasse.