Trying to understand the big picture... OK, once you ran the test, updated JIRA ticket status, what happens to the test? JIRA ticket gets closed, and the test that updates the ticket is no longer needed. What I'm hinting at is that test automation is used for tests that will need to be re-run over time, multiple times. So the life cycle of your test is limited by the life cycle of your ticket.
I mean, if it's worth for your organization to write automation per ticket and then discard it, go for it... If a JIRA ticket in question is going to stay open for a while and you need testing in the meantime maybe... In a TDD of a web app situation you could possibly even track the progress of a feature development by running a long scenario and see what failed.
If you want to keep you test code for regression testing after JIRA ticket is closed you will need to remove JIRA updating code from each test. Seems like a lot to keep track of. As another user suggested, why not let the human update tickets?