Should non-WordPress data get its own DB?

WordPress uses a prefix by default just in case the database is being used by more than WordPress. Since creating a new DB is pretty simple I would go that route. You would get the potential benefit of it being something separate that you can easily export, import or blow away if needed and also the potential security benefit if your WP site gets hacked this DB is separate (and vice-versa).

If you do decide to use the same DB then you should prefix your tables to make them easier to know what they are used for.