JD-EE;
The sidestick position symbol is only displayed on the PFD during takeoff.
I know about the small "stick" in the middle of a laptop keyboard - I think the HP has the same arrangement.
I think there is no connection between the way another control device might work and either the yoke or a sidestick in terms of muscular or cognitive habit which would confuse or alter a psychomotor response, even under stress.
If anything, the response would more likely be exaggerated, but in the correct direction. In fact I have always thought that that's where the initial two stall warnings came from right after the AP disconnect...a strong, quick pull on the stick, followed by a relaxation, (unloading, to use Retired F4's term). The continued aft stick after the stall entry is another matter I think. One considers the Airborne Express DC8 accident when thinking about this. (That said, we will never know why the Colgan captain pulled instead of pushed the stick; the explanation has usually been the notion that on that particular design, the T-tail can stall in icing, (several (NASA?) videos were referenced) and the unloading of the tail (stalled tail) would pitch the nose down. The response was to pull back, (not sure why, if the tail was "stalled" but there it was)).
I've flown in both seats while teaching and there is a difference when switching sides if one doesn't do it often. We've had the discussion about who was sitting where and why, (who replaces captain, licensing issues, First BEA Report, etc).
While possible, I don't think that played a decisive (primary) role here. But because sitting in one's familiar physical place does have a psychological and even physiological effect, (IOW, it does make a difference), I think the question of who was sitting where is still important for secondary, cognitive reasons. When one is not in one's normal seat, one needs to intellectualize responses somewhat, (think about the hand's position when reaching for a switch on the overhead panel, etc etc), rather than operating out of pure habit.
The poster who worked the mouse and typed with opposite hands makes an interesting point. There may be some minor similarities between this example and cockpit psychomotor skill but I think that that example doesn't fully translate in terms of analyzing or fully explaining cockpit behaviours. It doesn't take into account thorough training and the establishing of behaviour through long and frequent repetition both of which greatly reduce the effects of high stress and not being in one's familiar place.
That isn't meant to dismiss the effect; there is the need to examine it. My view has always been, the loss of airspeed information wasn't itself an emergency but it quickly turned into one due to the pitch up and we need to know why that happened. Large physiological responses are natural when under stress; is that what happened here? Perhaps the next BEA Report will address this, if so.
Part of the reason training is so thorough and realistic (up to a point, as sims can't reproduce 'g' or aircraft behaviour in unusual attitudes), is to reduce the effect of the sympathetic nervous system "fight or flight" response and provide ways built through habit, of controlling the stress response.
It is known that the stress response has a natural "pace" or curve where heightened senses and acute physiological responses quickly diminish under high, continuous stress. IIRC, the report on the Alaska Airlines MD80 stabilizer jackscrew accident off the California coast near LAX mentioned this. Whether this is a factor here would be something for the final report to comment upon.
To your question, I think an instinctual response which "confused" push and pull is not likely, given the complete/total absence of such a control movement/requirement in all aircraft. In other words, there are no QWERTY and DVORAK aircraft!
kind regards.