In discussing the option of Cal Ripken vs. Little League, the article in the paper stated that the kids that played Cal Ripken could also play Little League if they so choose. I have been told by some Little League parents that it is against Little League rules to play in another league while playing Little League so I checked the rule book.
2005 Official Regulations and Playing Rules for Little League states on page T-4: Participation In Other Programs- Little League, 9-10 Year Old Division, 11 Year Old Division: A player may participate in other youth baseball programs prior to the first game involving that player's team. Once play begins for a tournament team, players named on that tournament team's affidavit may not participate in any other youth baseball program until that team is eliminated from tournament play.
It appears that you can play both, however if named to all-stars, you must stop playing in one if you are playing all-stars in another. Looks like some kids will play both.