I've always thought the answer is "no" - after all the company makes no money from the stock price unless they issue new stock, and then they make money from whoever buys it then.
However there's a recent article (mirror w/o paywall) in The Wall Street Journal (i.e. the authors of which are presumably familiar with the financial markets) which seems to suggest otherwise. The title is:
Wall Street Steered Billions to Blacklisted Chinese Companies, House Probe Finds
And the first paragraph is:
A congressional investigation found that Wall Street used billions of dollars of American retirement savings and other investments to buy shares in index funds that included more than five dozen blacklisted Chinese companies.
If the picture in the first paragraph of this question is right, buying an index fund that includes the blacklisted companies doesn't seem like it does anything; in fact the Wall Street managers were doing their job of making money for their clients.
I'm wondering if WSJ is being sensationalist, or if there's something I'm missing.
Related: Does trading (or abstaining from trading) a company's stock help or hurt the company? which appears to deal with the general case, but not this particular one.