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An ORM (something like Django’s models or sqlalchemy) is a really helpful abstraction to help map tabular data in the database to the objects its being used to model in your code. It won’t help with connecting to databases provided by the user since you won’t know what the schema of the database is you’re connecting to, nor what you are going to receive back from a query.
With django, the database defined in settings.py is used to store information related to your app such as user credentials, migrations as well as whatever else you define in your models.py files. So definitely don’t try to change that dynamically as it is being used to store the state of your application for all users.
If you need to connect to external databases and run user-supplied queries, you can do that inside a view using the appropriate database driver. So psycopg2 for postgres would be fine.