[jmkupka]

the comment about "immediately participating in the game" is what I think most complicates what is an incredibly simple rule.

A player is "participating in a the game" by just sitting on the bench, waiting for her at-bat, which could be as many as 8 batters away.

For a DP, she is "participating in the game" while she sits on the bench as her team is getting beat up on defense for a 1/2 hour, and her at-bat is up to 8 batters away.

If she's in the batting lineup, she's "participating in the game". Period.