It is a terrible idea. How would you even reach those selection of players? There is literally no qualification, as all you say would be needed to download your ... free to download game. Anyone "wanting" to playtest your second part, can get qualification.
Also, downloading a free game is not claiming it, unless you do some things with sales and claimable properties. It will not be listed under purchases, just because it was downloaded.
Maybe organizing such playtests in discord would be a thing to try. You could also use any filehoster and have more control there over the distribution. But having an unfinished game on itch is rather normal. So why make it exra complicated. Why would I even want to download chapter 2, if I did not have played (and liked) chapter 1.