One of our cars has the accelerator ("gas pedal?") not physically connected to the engine at all - it's "drive-by-wire" to that extent ...I wonder if the affected Toyotas also have that?

Toyota has pinpointed the issue that could, on rare occasions, cause accelerator pedals in recalled vehicles to stick in a partially open position. The issue involves a friction device in the pedal designed to provide the proper "feel" by adding resistance and making the pedal steady and stable. The device includes a shoe that rubs against an adjoining surface during normal pedal operation. Due to the materials used, wear and environmental conditions, these surfaces may, over time, begin to stick and release instead of operating smoothly. In some cases, friction could increase to a point that the pedal is slow to return to the idle position or, in rare cases, the pedal sticks, leaving the throttle partially open.

http://www.toyota.co.uk/pedal-recall/index.html

I wonder if that makes it any more or less likely to get stuck...?

Toyota's solution for current owners is both effective and simple ... The company has confirmed the effectiveness of the newly reinforced pedals through rigorous testing on pedal assemblies that had previously shown some tendency to stick.