sql server batch execution sequence
No matter how many processors you throw at it, SQL Server will never "parallelize" across multiple statements in the same batch. It will completely finish update_query_1 before it starts insert_query_2, and it will completely finish insert_query_2 before it starts update_query_3.

Nothing about any of the statements in your batch is asynchronous unless you are talking about starting jobs, invoking Service Broker, or triggering some side effect. But none of these things would technically be part of this batch.