It appears that we could get bacteria to make some of our aroma chemicals for us, maybe even quite complex ones. Here's how Reshma Shetty describes the process. Maybe a natural perfumer could ask her to provide the smell of oakmoss without the IFRA restrictions.
[F]or anybody who works in a lab, who works with E. coli, when you grow cultures of the stuff, it just smells really bad. It smells really stinky, basically. And so our thought was, "Hey, why don't we reengineer the smell of E. coli? It'll make the lab smell minty fresh, and it's also a fun project that gets people, who maybe aren't normally excited about biology, interested in it because it's a very tangible thing. I can smell the change I made to this bacteria."
So the process was, you basically take a gene, we took a gene from the petunia plant, which normally provides an odor to the flower, and you place that gene into the E. coli cell. And by supplying the cell with an appropriate precursor, you make this minty smell as a result. So it's fairly straightforward.
Here's a long interview.