Will Apple Watch detect Sleep Apnea in real time?

It takes a minimum of a month of statistics before it makes a determination that maybe you have Sleep Apnea.

About 6 weeks after a co-worker got their Series 10 and started monitoring for Sleep Apnea, they were notified that they may have had Sleep Apnea.

So NO, it is not real-time.

Once you are notified, you should consult with a doctor, and maybe go in for more rigid testing.

My understanding is that it looks at trends in data:

Sleep apnea notifications on your Apple Watch - Apple Support

It will tell you if it thinks you should see a doctor. It's not a real-time alarm.