No, because with immortality, life loses his value. It loses it's value because what do we do with life? In life we do actions what makes us happy. Well, but if we have all the time in the world, what are the reasons to do it now? There isn't. If there isn't point of doing it now then we do not do anything. And if we do not do anything, our life has no value.
And if you live forever, in the end(phrase) you run over things to do, everything seems boring, and then you have nothing to do, only to wish you were dead.(But that is the thing you can't be).