>Putting this altogether, it seems there's an excellent chance that primitive uni-cellular life evolves pretty readily and multi-cellular animals tend towards increased intelligence soon there after.

How much intelligence though? Dinosaurs were around for eons and, as far as we know, never used simple machines or mastered the use of fire. So far, the human branch is the only handful of species that ever has. Even fairly closely related primates haven't figured it out despite the fact that they watch us do it all the time.