Hey Arnaud
I think is is definitely worth testing for UX and CRO purposes, and I don't think you'll do your pages "harm", from an SEO POV.
If the overlays appear onclick when in the category, and the rest of the category page is readable and crawlabe, it shouldn't cause any problems.
What's great is that you've already considered how you could rank those individual products themselves by giving them their own URL. Those might struggle a bit though if the URLs are not linked to directly from within the product category silo, or elsewhere on the site.
However, I don't see that as necessarily a bad thing. Unless you have a specific product type that sells very well and has significant search volume itself, I'd wager that most of your inbound organic traffic would best be served by the category pages anyway (IE, if searching for blue widgets, the category shows all the widgets you have, not just one type). That itself is more likely to match the user intent of those people entering your sites.
I would just ensure that you nail the tech and onsite aspects of those category pages - and the rest should be fine.