As a family member of two people who committed suicide (my father and my sister), I agree--this suicide note should be kept private UNLESS it pertains directly to the investigation into little Caylee's murder.
My father did not leave a note, but my sister left four notes--one to her husband, one to each of her two daughters and the other "To Whom It May Concern," presumably for law enforcement. To this day (she died this past September), I do not know what any of those notes said. It is none of my business, as none of them were directed to me.
That said, I do wonder if this suicide note that George wrote might contain information that would shed light on the big family secret that everyone seems so intent on keeping secret. You know, the one where Casey states, "Don't worry, I haven't said anything."