(I'm guessing that it is not done this way to avoid freezing, keep road debris from damaging the trap, and/or placing the outfall too low for the black water tank.)
Yes.
From what I estimate and read here, the "stink" factor of the grey tank is not a big issue and thus I may be able to get away with no trap
Yes again.
As long as you are mindful of what might go into the grey tank, and prevent it, it won't smell enough to warrant a trap.
Milk, meat, grain, food scraps in general will create nasty odors.
Showers, hand washing, and plate/pot washing (as long as you remove the majority of the food scraps first) will leave you with a grey tank that doesn't stink.
It should go without saying that the grey tank should be sanitized at least once a year, if not more often to prevent bacteria from growing (bacteria=stink).
Rob
Waiting for "someday" will leave you on your deathbed wondering why you didn't just rearrange your priorities and enjoy the time you had, instead of waiting for a "better" time to come along...