Does the Apple Watch work when you have tattoos?

Permanent or temporary changes to your skin, such as some tattoos, can impact heart rate sensor performance. The ink, pattern, and saturation of some tattoos can block light from the sensor, making it difficult to get reliable readings.

This still applies to all watches. For more info, see the 'What else affects your heart rate reading' section in:

Get the most accurate measurements using your Apple Watch - Apple Support

Depending on the tattoos, wrist detection may also not work properly, resulting in having to unlock the watch every time you want to use it. I'd suggest you see if they will let you test one out at your local Apple Store.

You can turn Wrist detection off but there is a downside;

Turning off wrist detection affects these Apple Watch features:

When you use Apple Pay on your Apple Watch, you’ll be prompted to enter your passcode when you double-click the side button to authorize the payment.

Some Activity measurements are unavailable.

Heart rate tracking and notifications are turned off.

Apple Watch will no longer automatically lock and unlock.

Apple Watch SE and Apple Watch Series 4 and later won't automatically make an emergency call even after it has detected a hard impact fall.