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EvelynM comments on Funnel plots: the study that didn't bark, or, visualizing regression to the null - Less Wrong
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Do I get your main point correctly that: If all studies were published the line in the upper graph would meander around the 1 line, but because all points fall either above OR below the 1 line, we can assume only studies that showed positive results were published?
Is it possible to put a bounds on the number of studies|same size that were NOT published, if we assume an equal likelihood of a point being on either side of the 1 line?
Yes.
I'm sure you could, since it's just estimating the other half of the distribution. But you're really going to need that assumption, which is not necessarily safe (eg. imagine flipping a fair coin - by a magician who unconsciously wants it to come up heads. It'd fail a funnel graph but not because of publication bias. And there are many ways to hire magician flippers).
If the statistical significance of the studies are valid, then it's quite unlikely that the lines would cross the x-axis. What Ionnidis is demonstrating is an overstatement of effect size in the initial studies.
Also, Yvain's point that a cumulative odds ratio graph is different from a generic funnel plot.