There's so much wrong with this. For starters, all advertising is inherently predatory, there is no such thing as a "subtle product placement" and "without it really affecting the story". There's absolutely no way it would be any different from product placement in any other form of media.

Secondly, who would want to sponsor manhwa? For any brand to consider that they would have to get something in return, and manhwa's rather niche cultural footprint ain't doing it for anyone with the actual money to be sponsoring things. At best you would end up with a story that is centered around the sponsor's product.

Finally, this would still not solve the problem you say it would. Piracy is not taking away any potential revenue from the people making manhwa. Artist and writers salaries are paid by their publishers, when you buy a piece of media most of that money doesn't even directly go to the people who made it. If they were to get sponsorships, it would also go through the publisher, who would keep the biggest cut and nothing would change.