The Barnsley Fern was constructed specifically to resemble the species of fern that it does. There are versions of it that have been modified to resemble other ferns. The fractal isn’t some secret mathematical code for why ferns look like they do, it’s more like a drawing of a fern. If someone made a fractal to look like another leaf, it would be just that, not an advancement into the secrets of botany.
The short answer: no. The two do not connect beyond the fact that ferns have a design reminiscent of a fractal, which is likely what inspired the fractal’s creation.
How “real” is it? It is a real set of functions, but if I design a set of functions to look like William Dafoe, it doesn’t mean I’ve cracked the matrix code into his genetics.