I agree with Joe. There are factors outside of the number of people in a company that determine it's success. Perhaps the more appropriate fact could be found when you think about a company's ability to successfully support a staff of 20 or more and still bring in good profits. I don't think the success is solely dependent on the number of people you have, the number of people you have is dependent on your success.
Given what I have said above, it would be true then that with a larger staff you can support more projects, broaden your offering or simply scale your existing offers, run your business more efficiently (assuming you have resources dedicated to ensuring productivity) and so forth. With more resources, more can get done and the faster you could potentially move forward.
So, while it is an easy fact to say generically, companies with 20+ employees are more likely to be successful than those with fewer, I don't think it really addresses the reason businesses of larger size are successful. Generally, they have more funding and resources and can take on a little more risk than a smaller operation. You can see the diversity in successful companies by looking at how business websites, newspapers, and other publications classify them. One method is certainly by employees, but another common filter is by revenue.