Upvote:6
It looks highly unlikely. All we can say for sure is that there doesn't appear to be any evidence that such a thing ever happened during that era.
The vast majority of our exemplars of Indus Valley Script were made on pottery or engraved into stone, particularly stamp seals. Of those, the majority appears to have been on pottery. However, I've also been able to find references to the script being found on tools, tablets and ornaments. Host materials reported to have been used are terra-cotta, ceramic, stoneware, glazed faience, shell, bone, ivory, sandstone, steatite, gypsum, copper alloys, silver, and gold. Intriguingly, some of the exemplars on pottery appears to be post-firing graffiti*.
Of course Thornwald is right to point out that this was so long ago that any biological host material would almost certainly have not survived. However, he should have stopped there. Absence of evidence may not be evidence of absence, but it is certainly not evidence of presence!
The next question might be, did they have access to cotton? Well, yes they did. Cotton cultivation in the Indus valley system actually pre-dates the Indus Valley Civilization and its script.
Where the problem comes in is that our first actual evidence of writing on an organic material in that part of the world doesn't come for more than a thousand more years (500BC). When it comes, its on palm leaves, not paper or (cotton) rag-paper. Paper wasn't widely used on the subcontinent as a host medium for writing for more than another millennium after that (sometime between 700AD and 1000 AD).
So there doesn't appear to be any good evidence backing up that claim of cotton-paper writing in the Indus Valley script.
* - Its tempting to speculate that this unusual use of pottery indicates that it was the cheapest writing material available in that area at the time, which would be evidence against any kind of writing paper existing. That's just me spitballing though, and there are probably other possible explanations for that quirk I haven't thought of.