Will my alarm still go off in Do Not Disturb?

It'll ring, but how loud depends on the Ringtone and Alerts slider in Settings > Sounds & Haptics. That slider is the alarm volume. If it's turned right down the alarm still goes off, just very quietly, and it looks like DND ate it. This is only true for Apple's own Clock alarms. Third-party alarm apps go through notifications and can get muted.

It does go off. Alarms set in the Clock app ignore Do Not Disturb and every Focus mode, and the silent switch too. Same if you use the Sleep schedule in the Health app.