I doubt anyone would proceed with a design that was so affected, but I can conceive of a case where to get just under an ICAO noise threshold you need to get just a bit further from the ground faster, since the takeoff profile does affect the noise levels. So, conceivable, you might find that the last 1000lbs of TOGW dropped you into the worse noise category, and so you';d rather take the hit on TOGW and keep a "clean" noise qualification?
In such circumstances you might have a placarded TOGW that wasn't driven by anything other than the technical cert, and maybe it'd be an option, just as some business jets have placarded MOGW Limitations purely to allow operations into certain airports, and some airlines use placarded TOGW restrictions - again, actual optional placards - to get lower landing fees.
But, as i said, you wouldn't plan to be there for a new sheet design, it sounds more like a "curses, we didnt expect that result and its too late in the programme to redesign" situation to me.