In practice this is just a one-time setup. We use
https://github.com/jneight/django-db-geventpool which uses psycogreen under the hood. It isn't perfect (we're currently tracking down some rare cases where connections aren't properly returning to the pool, though we believe this to be error on our side) but it's more than sufficient.
While making the ORM async capable would be great, I'm not sure it will ever make sense to migrate towards sprinkling "async" explicitly across our codebase. We'll see, of course.