Anything with a circuit board and can motors will run just as well off DC as AC.
This is because the AC is rectified to DC before it does anything useful. Polarity is not an issue because the rectifier will correct it.
This, as GRJ says, is clearly not the case.
The first thing is with any TMCC or legacy engine, the signal requires a low frequency carrier wave, The 60 cycle of standard US power works fine for this. I think you could get around this in a few creative ways, but haven't proven that yet.
The second thing is that polarity does tend to matter on many boards. The designers took the cheap/easy way out and used a single diode for half wave rectification. A full wave bridge will allow dc to pass through from either polarity, but a single diode rectifier will only allow power to flow from one direction. It won't cause damage with polarity reversed, but it won't work.
Next you have the triacs. Anything that uses triacs, or SCR's, in the electronics will not work on pure DC power. Triacs are great for controlling high current loads like motors and smoke units, but they have one big problem. They can not be turned off. Triacs depend on the power being supplied to them being shut off before they stop conducting. With AC this is not a problem, because the power shuts off 60 times a second as the wave crosses zero. With DC power supplied, once a triac is turned on, it will remain on. This is a problem for things like the smoke or light controls on a R2LC, and can actually cause damage if triacs are used in the motor driver H-Bridge.
In theory, you could use pulsed DC to remove the risk of damage, but the speed control or smoke volume adjustments would be off from how they were designed, as they would effectively be receiving a PWM signal rather than a portion of the AC sine wave with different amounts of electrical energy. This is something I might play with some day, using a high current transistor or Mosfet to cycle DC power off at something like 60 cycles, and see if TMCC engines could be made to run on such power. Again, a neat project, but just running AC is probably a lot simpler unless there is a specific reason for wanting to use DC.
Now, If someone took the time, I bet each triac in use could be replaced with a transistor or mosfet that would do the job on DC power, but I'm unsure exactly what would be involved. I've been kicking around trying to design a direct drop in replacement for the R2LC board that worked on the 2.4GHZ band,removing the sometimes problematic track signal from the equation, and would probably use DC compatible components if this ever comes about. I think it would be neat to have full TMCC control available for battery power locos and such.
JGL