Moreover, this linear distortion takes place with objects located close to the camera but it does not apply to distant objects.
It's not generally true to say that it "does not appy to distant objects". Distortion curves in optical data sheets are usually presented for infinite objects. Depending on the optical system, distortion may be better or worse with decreased object distance. Have a look at http://toothwalker.org/optics/distortion.html
Certainly, looking back to photos I took years ago with that front-of-lens converter on my Minolta, there are gobs of rectilinear barrel distortion for relatively distant objects - such as a window frame at the other side of a large room.
I wonder if you shoot the starry sky with fisheye will you get any rectilinear distortion? Probably not, coz all the stars are so far from us that no perspective distortion could take place.
I've done this; I love to do it - see the attachment below. You get severe
rectilinear distortion - of the coordinate grids which we use to describe stellar positions. But of course you cannot see those. You get no visible
distortion because the stars themselves are point sources, not linear ones. But even if the image has no visibly distortable content, the lens projection is still distorting like hell! If the quarter-phase moon was in the shot, for example, it would not be reproduced with a straight-edged terminator.
Again, when you say "will you get any rectilinear
distortion? Probably not, coz all the stars are so far from us that no perspective
distortion could take place", you are clearly confusing perspective and rectilinear distortions. They are completely unrelated.
[As a side issue: one can argue that the way that a fisheye renders the celestial sphere is actually a lot close to the way that the eye sees it. The scale magnification in the corners of a rectilinear ultra-wideangle shot stretches constellations and the angular relationships between stars in a visually odd manner. That's the price for keeping lines straight, when projecting a large portion of a sphere onto a plane sensor or film.]
I will buy H20 some day and make pics with converter on to show if there is any distortion. Probably I need not 2x but a kind of 1.5x converter to get full-frame with minimum distortion for close objects. If anyone can make such pics right now that would be great.
I'm not saying that it cannot
deliver good results - just that I am doubtful based on my past experience. I am genuinely interested in how this converter would perform, especially at wide lens apertures. Maybe they've got better over the years. Could you point us to a link for the type of converter you're thinking of getting?