I'm not aware of that, and frankly doubt it. I'm not even sure that Darwin read Smith. (I think there's a lifetime reading list for Darwin around somewhere but I don't know if it's on the net.) However in general Darwin did read much of the Scottish economists and was quite interested in the subject. He was also a very shrewd investor who multiplied the family fortune several time over.
It seems he did. In Descent of Man, chapter 4, he wrote: "Adam Smith formerly argued, as has Mr. Bain recently, that the basis of sympathy lies in our strong retentiveness of former states of pain or pleasure." There's a footnote (#21) that says, in part: "See the first and striking chapter in Adam Smith's 'Theory of Moral Sentiments.' "
Source: here. (Search on "Adam Smith" to find it.)
Your version is supported by Stephen Gould, in Eight Little Piggies (paperback, p. 148.) Gould says the influence was indirect, and came from reading the Scottish economists. A distinction without a difference. Smith's invisible hand is evolution directed by natural selection.