If you showed up at impound w/ the cooler there, but disconnected I would commend you for being honest and go on to worry about other things.

I can see the advantage on very few occasions during a sprint race. Longer races, yes, I can see you wanting to keep the oil cool rather than buying new guts for the diff.

If the R&P and LSD system you are using comes standard w/ an oil cooler I would consider arguing it. "Any final drive...." "Any limited slip..." provided they fit w/in the stock housing w/o modification. That is where you will have problems, getting the oil in & out w/o drilling holes in something. But if the "Gnicar TSR" brand ring & pinion comes standard with an oil cooler, well its part of the system. Isn't it? How is that different than the aftermarket ECU that utilizes a MAP sensor that gets tapped into an otherwise blank hole in the manifold? There is an allowance for the MAP sensor now, similar to spherical bearings that after a few years of people using the loophole the ITCS was altered to allow it.

Considering I got my log book written up for a carpet hanger being missing where it doesn't say I can remove it, I say this is no more of a stretch in the other direction.