If we were to remove the words 'religion' and 'G-d' from the equation, yet we're directing our thoughts towards an individual, might the affirmation of a 'connectivity' with others be beneficial? Some scientists and physicians believe so.
Well-being is often derived from emotional support. Emotional support provides comfort, ergo, calm or peace and when we are within that circle we undoubtedly are capable of feeling better. Feeling better allows the body , when it can, to heal.
This is more of a rhetorical thought. Personally, I indeed would pray for anyone I felt compelled to - the vehicle that carries that will can be called anything one chooses - the name is only a word, but the power behind it to this day remains a mystery.
Even a Bible passage paraphrased alludes to this - 'I lift up mine eyes to the hills from whence cometh my help...' Then the writer states '...My help cometh from the Lord.'
And from an entirely different perspective I suppose you could run up to the bed of a dying atheist and shout as they're taking their last breath 'Na Na Na Na Na Na, I said a prayer for you and there's nothing you can do about it!'
The great psychoanalyst Carl Jung, as well as Sigmond Freud closely studied the science of 'connectivity.' Dr Jung stated that the science was such that he could not discount the fact there was an anomaly to the statement there is no ability for people to connect. He died with those very notes being on his desk.
If we interject humour into it, I remember the story of the late WC Fields, an avowed disbeliever. His agent came to visit Mr Fields when he was dying and was surprised to find him sitting in a chair with an open Bible in his lap. Shocked, his agent asked 'Bill, what are you doing with a Bible> You're an atheist!' To which Mr Fields replied in his inimitable style, 'I'm trying to cover all bets!'
Finally, if I 'were' to find myself compelled to pray for an atheist, whether requested or not, I suspect my prayer would be that the individual did not leave this world alone or frightened.