Can a player who stops the Charleston still offer tiles in the optional pass?

Yes, in American Mah Jongg a player who stops the Charleston can still offer 1, 2 or 3 tiles to the player seated opposite. Whether the player opposite wishes to swap tiles with this player is another question. Generally, if a players stops the Charleston it signals that they are close to achieving Mah Jongg, as they do not have 3 tiles to pass. Therefore, it can be risky swapping tiles, as you may help them get closer to winning.