I think it's a bit more complicated than that. However, my overall impression is that engagement with management, followed by resolutions/voting/proxy-battles, followed by divestment as a last option, is a dominant strategy than just blanket divestment.

Second, even if small companies did suffer through divestment there is nothing to stop the larger fossil fuel firms simply using their cash flow and borrowing capabilities to purchase their now cheaper and more vulnerable rivals. So rather than divestment hurting the large amoral multinational fossil fuel companies and its remaining investors, it provides an opportunity for them to control and consolidate the industry further, potentially reaping more dividends from the act of consolidation.

Ironically, it appears divestment creates perverse incentives for people to invest more in fossil fuels.