Not yet, as far as I know, but perhaps someone will find a way to do that in the future. We're talking about the next two decades here, a lot can happen in that time.

DNA itself can be thought of as a language which describes proteins, and I personally don't know enough about the limits of LLMs as a technology to claim that it can never be adapted to, say, do reverse translation from desired protein shapes into DNA sequences.

This is why it's better to call the underlying technology transformers rather than 'language model'. It can make a model from anything you can digitize and is informational (random noise would not be informational for example). It's the relations between the bits of data that matters.