The original question is still a little light on specifics so I'm going to base the answer on the second generation Outlander which, as cited, uses the AWC electronically controlled 4WD:
When “4WD Auto” mode is selected, the Outlander's 4WD system always
sends some power to the rear wheels, automatically increasing the
amount under full throttle acceleration.
So selecting this mode immediately changes the torque to the driven wheels, transferring some away from the front wheels and to the back wheels. This will change the weight transfer of the vehicle under acceleration and engine braking. This will also induce greater transmission loss as driving four wheels requires more interacting moving parts than 2WD. This will be most obvious under engine braking.
Some important aspects of the original question, however:
I specifically mean when I'm travelling at a steady, low speed in a
straight line over an even surface
In the real world, there is no such thing as a straight line over an even surface outside of an auto-testing facility.
but with my car's frame being a rigid body my intuition tells me that
this shouldn't be possible.
Your car is not a rigid body. Nothing about a car is truly rigid, including the frame. Remember, you are riding around on a system of linear and torsion springs, the oscillations of which are all damped differently.
Now, given all of the above, it is also important to remark on one of the comments:
I seem to be able to perceive through my bottom on the chair that the
power is coming from the back as well as the front
It is critical to remember that the butt dyno is well documented as the least accurate instrument in the vehicle.