When connecting to a SQL Server Asynchronous Processing=true is required in the connection string to enable true async support, is the same true for Npgsql?
No, this is a SQL Server-specific connection string parameter which doesn't exist in Npgsql (you will get an error). Npgsql's supported connection string parameters are listed here.
By the way, Asynchronous Processing doesn't seem to do anything on SQL Server anymore either, see the docs.