If life lacks any meaning and we react in the way Camus wants us to then we can focus on other things and personal human projects. Does this mean that immortality becomes desirable?
From a purely logical perspective, the question is not answerable.
The desirability of immortality does not stand in any necessary connection with whether life is absurd or meaningful.
Syllogistically, you are asking if A=B, does C=D follow?
So what is necessary is to add some premises which link meaning or lack of it to desirability or undesirability of that state of affairs.
Here's some further things to consider:
Would living a meaningful life, though in perpetual agony, make immortality attractive?
Is there anything about absurdity that makes it desirable or undesirable, or do other factors come into it?
If life is absurd, immortality might be a continuation of the absurdity - and worse, because life ends but immorality goes on for ever. An eternity of absurdity! What a prospect.
However, if immortality provides an extension of our ability to 'focus on other things and personal human projects', then it looks attractive - unless the other things and projects drain themselves of interest eventually and nothing new and absorbing can take their place.
Camus asserts what he regards as self-evident facts: that we must die and there is nothing beyond this life. Without mentioning it, Camus draws a conclusion from these facts, namely that the soul is not immortal. Here, as elsewhere in his philosophical writing, he commends to his readers to face a discomforting reality squarely and without flinching
The Camus' conclusion is based on the premise that immortality is impossible. Therefore the desire of immortality is part of the absurdity of life.
We all know that 'Man is mortal'. We need not desire for mortality. So the thing we can desire is to become immortal. There may be personal difference in the idea of immortality. We can't deny this even if the truth is something else. It may be an immortality that transcends this absurd life. But only those who believe that there is something immortal would desire for it.
Usually, "desirable" means "desired." This is in no way contradicted by an absurd universe: you want what you want. Anything, including immortality, can be desired and so desirable.
It is sometimes used to mean "that which is a proper object of desire," as a synonym for "prudent," "wise," or "beneficial." In that sense, an absurd universe would make all things not desirable, because nothing is wise, or prudent, or beneficial except as (absurd) stopgaps against the absurdity of the universe. Including immortality.