No, that's not how it works. I'm afraid that's your theory, which is not correct.
Their theory is far more interesting, and less retarded. Single celled organisms are more likely to clump together to avoid certain types of predation. That has actually been observed in a lab, by the way, as, I believe, has the way they then form different sorts of cells on the inside and outside of the clump. Much like multicellular organisms do. Its very, very primitive, but it is the start of multicellular life. What, you expected a cat to fandango its way out of the primordial ooze?