The assignment urgency does not impact the deadline and passed deadline intervals. The value can be used by your processes to get next work based on the urgency value or you may have other logic where you route and report on work based on the value.
So that doesn't really answer the question. Nor can I find reference to it in the CSA course. Is a notification sent out? does it prevent the case from advancing until the assignment is resolved?
from another site:
->The assignment urgency is used by Pega to select assignments for users from team or department queues. ->When a user queries Pega for their next assignment, Pega identifies all of the assignments that the user is qualified to perform and selects the assignment with the greatest urgency. ->Once the urgency reaches 100, Pega ignores any further urgency adjustments. ->When this occurs, other service level agreement behavior is unaffected. ->For example, a deadline interval is configured to increment assignment urgency by 30 and notify the assigned user that the deadline has been exceeded. If the assignment urgency is 100 when the assignment reaches the deadline, Pega ignores the urgency increment but still sends the notification.
The urgency of an assignment is capped at 100. However, all other processing continues - if an assignment is created with an urgency of 100, the urgency of it will never rise, but any actions configured for the Goal, Deadline, and Past Deadline events would still occur.