sure, you can trigger a replication job immediately via CM API.
In Python, you can find ApiService class inside endpoints services.py, which has function trigger_replication_schedule. You need find the service (hdfs or hive) first, and call the function with a schedule id, like:
hdfs_service.trigger_replication_schedule(schedule_id, dry_run)
It returns the corresponding command. If you want dry run, set the 2nd parameter to 'True', by default, it is 'False'.
Hope this helps.
-Lei