[orange4boy]

I'm sure there's a mechanic out there who would try to convince me otherwise (and it would take a detailed explanation to convince me) but I believe it would take a long time for the bearings in a transmission to run dry. This is the only damage that I know of that can happen to an auto transmission in EOC. I think this idea of auto transmission damage comes from towing. Those motorhomes you see towing a car over long distances could cause the bearings to heat up, dry out and cease. The differential is indifferent (ahem) to this effect because there is an oil bath and nothing more. No pumps reliant on the engine. There might be damage to the diff and U-joints from the different RPMs of the engine and diff at road speed when put back into gear after EOC but you can mitigate this with a tach by revving the engine to the correct rpm for the gear.

I'm not an engineer but this is what I believe from my own understanding of lubrication. There is this idea that if your oil light comes on your engine will "blow up" (cease) instantly but I have witnessed engines run for hours with no oil going through the oil pump. In certain circumstances like drag racing where the engine is at maximum output and all the parts are under extreme pressure catastrophic failure might happen if oil pressure goes south.

Having said all this, you would be wise to make absolutely sure with your own vehicle so you don't blame me later if your tranny bites it while EOCing. Plus, I don't actually do it if anyone asks. This is all theory, you understand...

Added: I just realized you may be talking about a front wheel drive unit which has a built in differential so all bets are off there although I still believe the seconds of power off involved in EOC are trivial to wear in the drivetrain. RPM differential is another issue.