"Beware the Jabberwock, my son! The jaws that bite, the claws that catch! Beware the Jubjub bird, and shun The frumious Bandersnatch!" - from Jabberwocky, by Lewis Carroll
I'm certain that if we ever sequenced DNA from the frumious Bandersnatch it would match hypothetical and putative proteins.
Why? Because we always (well, almost always) get matches to hypothetical and putative proteins when we do a database search with a protein sequence.
Why? Because many of the protein sequences in GenBank (at the NCBI) are a result of conceptual translations.
A conceptual translation is where we feed a DNA sequence (or often an mRNA sequence) to a translation program. The program "decodes" the sequence and determines the possible amino acid sequences that could be produced from that nucleic acid. If we have a DNA sequence, we could have six potential amino acid sequences, since we could decode either strand. If we have an mRNA sequence, we have three potential amino acid sequences. We make our best guess which sequence is right, and submit that to the NCBI as a hypothetical or putative protein. The protein remains hypothetical or putative until there are other data to show that it really exists.
How do we do that?
With the genes that I sequenced, I did this by cloning the sequences into E. coli, producing the protein, making antibodies to the protein, and using the antibodies to demonstrate that the protein could be found in the organism. I think mass spectrometry is one of the additional methods being used today.