Had Arwen sailed for elvenhome, whither Aragorn?

[Imladris]

Well, I have always considered Aragorn to be "beyond" us, more noble than any of us could hope to be. I believe this sentence sums it up:

They [Aragorn and others] are our superiors. We are meant to view Aragorn as a lord..etc

-- Credenda/Agenda, Flotsam, Volume 14, Issue 2

So, taking that "definition" of Aragorn, I don't believe that he would have been put off doing his duty by the fact that Arwen decided to go to Valinor. It would have been against his nature, against his nobility.

Of course, the knowledge that Arwen awaited him at the end was definitely a bonus, but I don't think that he would have been deterred from battle.

As for Eowyn, I think he had a definition of love so strong that he could not violate it by marrying Eowyn, a woman he did not truly love.