Not really. From Apple about sleep monitoring is the following:
Review your sleeping respiratory rate
In watchOS 8, your Apple Watch can track your breathing rate as you sleep, which can give you greater insight into your overall health. After wearing your watch to bed, follow these steps:
- Open the Health app on your iPhone, tap Browse, then tap Respiratory.
- Tap Respiratory Rate, then tap Show More Respiratory Rate Data.
- The Sleep entry shows the range of your respiratory rate as you’ve slept.
Note: Respiratory Rate measurements are not intended for medical use.
But I would not interpret this as a true measure of Sleep Apnea. And there is no specific notification which suggests you have sleep apnea. If you want to know if you do, ask your doctor to set you up with a test in your home. There are several companies who send out kits, where you attach electrodes to your chest and a finger oxygen sensor, which very accurately measures for sleep apnea. I knew I wasn't getting a full restful nights sleep and one of these test kits revealed I was having up to 400 apnea episodes per night. Needless to say I now sleep with a CPAP machine and I monitor my score every morning when I get up. I'm now averaging less than 6 apnea episodes per night and I wake up fully rested. Best thing I ever did for my health.