Yes. This was my point, early in the thread, when I pointed out that the possibility of infinite human lives blows Carter out of the water. Whether we draw the 7th ball or the googleplexth ball, we're equally unsurprised to find ourselves close to the start of human existence.
Freeman Dyson certainly did some work in which he suggested that the number of "processor cycles" possible in a finite, expanding, cooling Universe approached infinity as time went to infinity. This would suggest that there would be room for an infinite number of human consciousnesses (implemented in some suitable form left as an exercise for the student) in the future Universe.
A Big Rip scenario might well undermine his calculations, however: I don't know.

Grant Hutchison