Yes, the example article I linked to on another comment has the name of the university and the download date watermarked. And that's on an article for a large, long-established journal; it's not like they're just missing watermarks on niche journals.
Thanks for the tip about tweeting. I need to set up another github account disconnected from my professional identity but that shouldn't be too hard.
EDIT: and maybe a separate Twitter account. And maybe both accounts used only from public wifi, too. I wouldn't put much past the publishers when it comes to getting revenge on people who help sci-hub. Unlike Elbakyan, I am not out of their reach.