No, not yet. I'll let Joseph give you his ETA on that... he recently picked up this work.
For now, your backend must be either Oracle or PostgreSQL.
Jopr 2.2 - slated to be released tomorrow - can only be installed against Postgres 8.2/8.3 or Oracle 10/11. However, MySQL support is the very first thing on my task list for in the 2.3 release time frame.
I'm hesitant to provide an upfront ETA without having done any development yet, but from some preliminary investigations this doesn't look like a terribly difficult task. A good chunk of the legwork has already been done by the community; my job is mostly to integrate that patch and enhance it as necessary to iron out the kinks.
I actually expect most of my time to be spent in testing to make sure I've converted every last item to work with MySQL properly. A rather conservative estimate would be a month, but I realistically expect to be done with this work much sooner. I've made a mental note to post back to this list when the initial stuff is committed to TRUNK.
Thanks for info