That wasn't the assumption I'd make. What I was saying in that hypothetical example is that a "supernatural" force actually was causing this to happen. That's not an assumption, it's a fact (something I have the luxury of imposing when coming up with hypothetical examples). So my question is that given that fact, would science be capable of recognizing it (regardless of what assumptions it starts out with initially)?
In the context of your hypothetical, you are presuming exhaustion of all possible physical explanations (you suggest, after all, that the supernatural explanation was not the assumption you started with). Indeed, to reach your conclusion that the supernatural explanation is a fact, it is a necessary prerequisite that you exhaust all scientifically plausible, physical explanations.
And (staying with your hypo), since science is the vehicle by which the exhausted physical explanations were necessarily explored and discarded, science would also be the vehicle by which the ultimate supernatural explanation was reached. So certainly -- science would be "capable of recognizing" (and indeed be the vehicle for recognizing) this supernatural explanation.
This, of course, renders your parenthetical meaningless. The starting assumption must be that there exists a physical explanation. If the starting assumption is the supernatural, you will never rule out or even examine the physical, and consequently your supernatural explanation will be inherently implausible.
Now, are you suggesting that science, as of today, has examined and ruled out all possible physical explanations for either biological diversification and development or for the genesis of the first reproducing organisms?