The question really says it all. Here's the autosave docs page: http://imperavi.com/redactor/docs/settings/autosave/
I'm just thinking about what would need to happen in order for this to work.
Craft would have to expose Redactor's autosave configuration somehow - either via UI or a Redactor config file.
You'd have to write a plugin and point the autosave configuration to an action on a controller in your plugin.
That action would be responsible for persisting the RTE content as well as the entry and field it came from (since you can have multiple RTEs on a page) - likely the database.
All-in-all, not a very robust solution. It'd be much more likely that we implemented our own autosave solution that worked for all fields at the entry level, instead of just the RTE.