No the cluster size isn't fixed, nor is the event rate — the clusters are chosen purely based upon what an "unusually long" time between events would be. That's precisely how the rate ends up canceling itself out. Given this formulation, the expected cluster size is always e, regardless of how you define celebrity. That's what makes it fun.

Now the human psychology part that this doesn't cover is that typically when you have two or three A-listers die, well, then you start seeing all the B- C- and D-listers that also died in the same period that you would have otherwise ignored.