Issue:

If an alert goes to a user as part of an Escalation Policy but that user has Quiet Hours enabled, the Alert should escalate immediately to the next user. It shouldn’t wait for the escalation time to lapse since no one has received a notification for the alert. Especially if the Quiet Hours for the first user on-call is going to run longer than the escalation time. 

Suggested solution:

Have an option in Escalation Policies to 'notify next user' if the current user has Quiet Hours turned on during the time that the alert notification should go out. 

Workarounds:

You can overwrite the Quiet Hours setting for urgent alerts by adding OverwriteQuietHours tag to alerts.