Yes, the jobid is returned when you start an asynchronous job:
https://rclone.org/rc/#running-asynchronous-jobs-with-async-true
Here is an example where I monitor a job using the group assigned when starting the job:
https://forum.rclone.org/t/c-code-for-rclone-copy/33990/13
You can also just request status based on the jobid returned when starting the job something like this (not tested):
POST http://localhost:5572/job/status HTTP/1.1
content-type: application/json
{
"jobid": 123
}