Regarding how cycle time is tracked in Jira, does putting a user story on hold "stop the clock", so to speak, on the cycle time attributed to a given user story?
Do you mean the information shown on Jira's interpretation of the control chart? If so please see this (emphasis below is from me):
Cycle time is the time spent working on an issue — typically, the time taken from when work begins on an issue to when work is completed, but it also includes any other time spent working on the issue. For example, if an issue is reopened, worked on, and completed again, then the time for this extra work is added to the cycle time.
Here is the reference for that information:
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