I think you’re right. You do (or, at least, when I imagine it in my head, I do) hear it frequently used when saying goodbye, but I don’t think it would be used to say goodbye.

If someone said ‘cheers’ to me when parting, I’d interpret it the same way as if they’d said ‘thanks’ — which could be slightly strange, depending on the situation.

https://en.wiktionary.org/wiki/cheerio

Maybe it is a conflation of cheers (smiles, thanks) and cheerio (old-fashioned familiar good-bye).