I'm pretty sure picking up the cue ball when you have fouled is allowed in the ACS. I think it is good sportsmanship to remove the cue ball from the table when you have fouled. To the extent that you are the referee once it is no longer your turn, it is your responsibility to remove the cue ball from the table.
On a related point, in general you are not allowed to just pick up the cue ball without shooting to pass your inning. In the video above, that's what Michaela Tabb's comment was about when Lương Chí Dũng wanted to simply pass his shot. Of course he thought Michaela would pick up the ball. She correctly required him to shoot. (He could have shot a better shot.)