Can spatial disorientation in low visibility situations lead a pilot to fly upside down?
The short answer is "Yes", if the pilot is not properly trained, doesn't trust their instruments, or has an instrumentation failure.

Without a visual reference (such as the real horizon or artificial horizon) it's very easy for a pilot to place their aircraft in an "unusual attitude" -- something other than the expected straight-and-level flight or commanded turn.
As humans we naturally rely on our inner ear and sense of balance to tell us what's "up" or "down", but in a moving aircraft you can move through a whole range of attitudes in "1G maneuvers" (where your body thinks down is where your seat is).
Little micro-movements we unconsciously make on the controls (or larger movements we may make consciously in response to turbulence or other perceved disturbances in the aircraft's attitude) based on what our ears and butts are telling us will eventually get us into trouble.

It's so easy that often instructors will have students create their own unusual attitudes in training by having the student close their eyes and simply try to fly straight and level - within a few minutes at most the student will invariably no longer be in level flight.



There's an exercise you can do on the ground to illustrate how imperfect your sense of balance and direction is, but it requires a large, flat, open area. We'll use an American Football field for this example:


Stand on one of the goal lines
Have a friend stand at the 50 yard line (about 45 meters away)
Close your eyes or put on a blindfold, count to ten, and walk directly toward your friend
Stop when you reach your friend (or your friend yells "STOP" because you're about to walk into a goal post)


Most people will not make it to their friend on the 50 yard line, because without a visual reference it's very hard to walk a straight line: You will veer off one way or the other, and some folks will even manage to walk in a complete circle (which is what eventually tends to happen over a large enough distance).
The same principles apply to flight, except there's a third dimension (vertical) to contend with.