Does the Apple Watch 9 work on a tattooed wrist?

Expanding a bit on what Bob said, the sensors that detect that your Watch is on your wrist and offer other functions can have problems with wrist tattoos. Your Watch may not reliably detect that it's on your wrist and other features may also fail. The only way around this is that some people have reported using epoxy bottlecap stickers on the bottom of their watch.

For more discussion on using wearable technology with tattoos, see:

https://www.theverge.com/23567992/wearable-tech-tattoos-fitness-tracking-how-to

Regards.

No.

Opaque ink blocks light, which is how the sensors work.