The child was asleep. I'm sure we all look a little funny if a camera caught those moments right before waking.

I'm pretty sure if the baby's face is the only basis for this theory that it isn't true. They showed Claire's relationship with the baby's father in the earlier seasons and the reason she wanted to get rid of the baby was because the father left her. I'm also pretty sure that in one of the early episodes Jack said to someone in Sydney that it was his first time in Australia.