Mobile app using PouchDB-CouchDB and MySQL-open source projects pouchdb/pouchdb
PouchDB running on Node can actually use any LevelDOWN-based adapter, and there is one for MySQL. I haven’t tested it. More info here: http://pouchdb.com/adapters.html#pouchdb_in_node_js.
However, this is probably not a good fit for your use case, because the data that PouchDB will store in MySQL will be totally different from the data your app is currently using in MySQL. In order to support replication, PouchDB keeps the revision history of every document stored (think git), which is different from a traditional database like MySQL, which just stores tables and rows that can be deleted/inserted/updated. Databases like CouchDB and PouchDB were built from the ground up to support replication, which is why this versioning system exists.
That being said, if you write your own sync layer between MySQL and CouchDB it could work in theory, but it would probably be so much work that you would lose the benefits of CouchDB and PouchDB’s built-in replication.