All workflow and orchestration engines are Turing complete, the whole purpose is to automate execution flows.
I don't think so. First, JIRA is not orchestration. Second, all workflow needs to do is associate some status with external information, and make it easy to manipulate those. You need triggers and rules, some thing like infinite counters, two stacks, a bidirectional tape, etc.
Prove me wrong!
How many of them can run infinitely? Or be re-triggered by humans to continue where they left off?