Will Postgresql statements execute synchronously if autocommit=true?

If a single application thread sends a series of INSERT statements and autocommit=true, will the statements be executed synchronously on the server? I read that on the postgres server side, "there is one client process connected to exactly one server process", but haven't found much more beyond that. I need synchronous execution to satisfy foreign key relationships, but I suspect the server (9.6) may run the statements concurrently.