Quite honestly, there isn't a lot at PI that kids will enjoy (unless they're old enough to be into dancing, etc). At one time it was a glorified street bar, now it's just sort of sad, but still has the feel of a bar spilling out into the street, in a much less 'glorified' way. I'd take the family to The Boardwalk for the evening, or spend your time at Downtown Disney instead. The one exception is Raglan Road, which is fabulous.
While I won't call anyone's offspring 'screaming/shrieking little ones', I have to agree having children at PI takes away from the adult atmosphere. They won't be kicked out, but having youngsters at Adventurer's Club does change the whole experience, and not for the better. Some of us need a shot of adult humor after a long day kissing Princesses and being sprinkled with pixie dust, and that won't happen in the one place it is SUPPOSED to happen, if children are present.
But again, Disney says it's ok for them to be there. However, your fellow club-goers are likely to cast unpleasant glances your way and judge you to be bad parents for taking the kiddies to a bar. If that doesn't matter (and it's your right not to let it matter), they'll certainly be allowed in. Just be forewarned....they won't be popular with the locals and even more importantly, they probably won't have as much fun as they'd have somewhere more suited to families.
I have two little kids, but when I go out to PI, I would rather be amongst adults 
