WEll no...they are called the imortal lands, not becoause the lands grant immortality, but becoasue of those who live there -
Valar, Maiar and Vaynar (Elves of Light)
One can die there too, but ones that do then go in the Halls of Mandos (which are located allso in Valinor, so basicly, weather dead or alive, all elves eventually come to Valinor).
As it is written in the histroy of middel Earth, at the end, Morgoth will return from the timeless night and the Final Battle will take place. And Eonwe, Tulkas and Turin shall defeat Morgoth in a battle that will destroy allmost the whole Arda. And Feanor shall come and unite the three Sillmarills and with them rekindle the light of the Two Trees of Valinor. And the mountains shall be leveled, and their light shall go over the whole world. And The world will be young again, and the elven dead shall arise. The Dwarwes will gather under Aule and they all together shall reshape the world.
But of men, the prophecy speak not - only that the gift of mortality Eru gave them will be the envy of even the Valar themselvs...