Hey neighbors! As @UncleBill stated, there are a couple of answers to this question. When using Do Not Disturb mode on your mobile device, your Ring app will not override it unless you have a Ring Alarm system and adjust the settings to override.
For non-Alarm Ring devices, do not disturb will prevent alerts as outlined in this help center article. If you have Alarm and are wanting the choice to receive emergency alerts with do not disturb mode on, this article provides the steps to change these settings. I hope this helps! 