We just purchased a new to us 2005 Honda Pilot to tow behind our MH, after a lot of research. The 2005 is the last "official" year Honda endorsed flat towing the car. Having said that, there are more than few people out there who tow newer generation Pilots despite the voided warranty. They apparently still have the same drive train and as long as you follow the towing procedure exactly it should work.
That procedure, involves starting the engine, shifting the tranny through R N D D3 D2 D1 D2 D3 D leaving it in drive for at least 3 minutes before shifting into Neutral and turning off the engine. Leave the key in the ignition to keep the steering wheel from locking, release the parking brake, then use your other key to lock the door (the remote key fob won't work with the key in the ignition) as you exit.
From what I understand this procedure engages the trans fluid pump, lubricates the tranny, and the pump is left engaged as long as the tranny does not go into reverse. So when it's being pulled the road the pump still moves fluid through the system.
So far_ so good for ours, but we have only towed it about 1,600 miles so far. The same applies for the Acura MDX from what I read as its the same drive train on both.
Hope this helps.
Tom