Technically, the player should have collected $200 before even landing on Community Chest. The text on the space says that you collect the money "as you pass Go", so the money goes to players passing Go as soon as they reach the space. If we really want to get pedantic, they shouldn't even continue moving (if the die roll indicates that they should move further) until they have the money.
In practice, it's unlikely that anyone actually picks up the money at the moment they land on the space, but the fact that they should collect it then still matters. They passed Go before the card came up, so they still get the money, because at the time they should have gotten it, there was no reason for them not to get it. The "Do not collect $200" on the card only matters if the character would pass Go after picking up the card, but before landing in Jail.