Ilúvatar's plans for Aragorn were meant to be in Middle-earth and to become the King of Gondor and Arnor. Also he would need the approval of Ilúvatar to make such a move if he were to sail west with Arwen.
Example:
Tuor was allowed to reside in Valinor because of Lúthien's will to give up her immortality to be with Beren, and through Ilúvatar Manwë allowed this action to happen.
So unless Aragorn had Ilúvatar's approval no such action could happen, not to mention the straight road to Valinor is only open to Elves.
