Assuming we can use SMEs as a proxy for closely held corporation (which seems reasonable enough given minimum sizes for equity sale and the relative rarity of venture capital-owned enterprises), not really. As of 2010ish, 68% of people in the US worked for SMEs. (Source, section 2.2) I am honestly too lazy to track it down more closely than not, but be wary of over-estimating the impact of publicly owned corporations.