This is a really interesting question! Holmes scholars, you may have a better idea here, but I'll give it a shot.
Darwin lived from 1809-1882 and Arthur Conan Doyle lived from 1859-1930. Darwin was a naturalist and Doyle studied medicine and eventually practiced opthamology. Given that they were partly contemporaries and that they were both living in the same country and that Darwin's ideas were revolutionary at the time (and still controversial for some today) and that both men were involved in scientific/biological careers, I would say it is safe to say that Doyle was certainly aware of Darwin, likely influenced by him.
He quotes Darwin in "The Study of Scarlet" (I think this is the right story):
"Do you know what Darwin says about music? He claims that the power of producing and appreciating it existed among the human race long before the power of speech was arrived at. Perhaps that is why we are so subtly influenced by it."
You could easily make the case that there is a general parallel between Darwin's gathering of information and Holmes' gathering clues. You might say that Darwin's inductive process incorporated elements of deduction along the way. In other words, like Holmes at times, Darwin began to inductively piece together clues and the idea of evolution and species adaptation began to develop. Then, he deductively began to organize and gather data to support that hypothesis. Holmes scholars would do better than I on this: But Holmes would recognize specific, detailed clues and inductively form conclusions; then, he would have an "aha!" moment and would then have the overall conclusion; then he would deductively put all the pieces together. I don't really think he got this idea from Darwin; it is just part of the scientific process.
Lastly, in terms of religion/science, Doyle was a Christian Spiritualist so his ideas of reality would probably contrast pretty starkly with Darwin's more scientifically based world. Darwin pretty much referred to himself as agnostic. Both extremely intelligent guys, so who knows; Doyle could have been as open to the most progressive scientific ideas as he was to Spiritualism. Check more bio on Doyle, inductively pick up clues; form a hypothesis. Then, deductively find the clues and organize the data to support your hypothesis.