So, as the title suggests: does distortion removal caused by lenses means that the parallax is also removed from the pictures?
No, these are unrelated. Distortion removal is a 2D mapping which moves pixels to remove barrel and pincushion distortion. Parallax correction requires multiple images or depth information for each pixel and is performed by completely different software algorithms.
if it is possible to view a number of scenes stereographically after the lens distortion is removed from them
In theory all distortion correction does is undo some distortion a lens introduces because it is not an ideal ( theoretcally perfect ) lens. You will note this distortion is radially symmetrical and the effect is most notable in the curving of what should be straight lines in the image ( for rectilinear lenses ).
This should, in principle, make viewing two images as stereographic pairs better as the distorted images would be more likely to cause (minor) discrepancies from what the human vision system expects than the undistorted ones.
The correction should, again in theory, make it more accurate for a tool that estimates distance from stereographic pairs. It is the distorted image that is more likely to cause problems.