I wonder what is its function and if it can be the genetic material for a living organism. If not, why?
Yes, double-stranded, helical RNA exists. It can occur naturally, a famous example would be Rotavirus, as well as synthetically in the lab.
Please note, however, that viruses strictly speaking do not qualify as a living organism.
As the OP asked for double-helices and did not mention dsRNA, I would like to point out a tool developed by my close colleagues, that predicts secondary structures of RNAs from sequence.
Here, base-paired regions are assumed to be in helical conformation.
You will see that most RNA sequences have some theoretical potential for auto-base-pairing with small, albeit temporary, helices.
Further, you asked about function of helical RNAs, which I more generally interpret as "structured" RNAs: Important terms or examples that you can further research are: 1."Rybozymes", which are RNAs with enzymatic functions; "Aptamers", which are RNAs found or created by SELEX that can bind biomolecules and even inorganic compounds with high specificity; 3. RNAs that have important functions in "RNA-protein complexes" as found in the ribosome, splicosome, telomerases, nucleases, RNPs and more..