Will Postgresql statements execute synchronously if autocommit=true?
With autocommit enabled each statement forms a separate transaction. In a single session (connection) only one transaction can be active at a time. However, transactions in multiple concurrent sessions can, and will run simultaneously. In other words, as long as you issue your insert statements using the same database connection they will execute serially.

Whether you do that in a single application thread or not is irrelevant, since it's possible to open multiple database connections in a single thread, as it is possible to reuse the same connection between multiple threads (with proper synchronization, of course).