I think that is very definite possibility. But there are some important differences between the fine tuning of cosmology and physics, and that of biology. The major one is that we have no answer (and might never have one outside of theism) for the fine tuning of the physical constants. In biology, many potential fine tuning examples are explainable from evolutionary theory. The perfect rate of mutation to allow for evolution, but also maintain the integrity of organisms is one example.
So the question for convergence is what is the mechanism. One answer has been simply (as I believe Roger said) that natural selection allows for certain characteristics that fit a limited number of available niches. Some neo Darwinians will use that one. I happen to believe (and I think Conway Morris does also) that answer is deeper than that. Fine tuning is one possibility, or there is something about the way life first developed on this planet that included a large degree of constraint (which is the mirror image of convergence) in evolutionary directions. Either way, there is no doubt a great deal of material here for theological reflection.