In theory an index fund should never own that much of a company, because that means it would own >50% of all publicly traded companies. The whole point is to spread the risk evenly so you can realize the average returns without having to put any thought into it. It shouldn't mean it's buying $100k shares of GE and also $100k shares of Mom&Pop Pickle Fork Inc.
Naively (ignoring other dynamics of index funds), sure, compared to 100% investors actively engaged in governance. But I suspect investment in index funds replaces largely hands-off direct investment and so, market wide, has virtually no average effect on that (though it may shift the effect among firms compared to those investors doing so directly.)