Last tested: Jun 23, 2017
No. Selecting "Update" on the License Key admin setting will only ping the license server. It should not impact any ongoing code changes and it should not kick off any PDTs.
The "Update" setting is used in the event that a user's license feature is already enabled but the end user cannot see that license feature on their instance. After clicking "Update" you will see the following message: "License verified and updated successfully."