Your density measurements wont be true to what the press is producing with an overprint. The press probably has a certain density target that you're looking to hit, say 1.2 for cyan (whatever the case may be) - you may be at the 1.2 , but with the overprint maybe it's measuring 1.5 - a new operator on the press might be tempted to bring down his or her density based on the incorrect value. Or, maybe you're expecting the extra saturation and know that a 1.5 is really about a 1.2 in reality.
Personally i would like the overprint removed from the color bar area. what if the overprint fluctuates or piles up in the tail area, your density could appear all over the place when in actuality it's stable and the aqua coating that's making it appear that way.