The details will depend on the exact implemention, but I don't think this necessarily effects output quality.

The models "natural" output is the result of a series of random numbers. The watermark works by biassing that series towards a different series of numbers. Assuming that second series is cryptographically secure psuedo-random, the even distinguishing the biased sequence from true random would be impossible with compromising the key or prng.

As an extreme, suppose your prompt was public, and the model seeded its PRNG with a secret key instead of a genuine random seed. Such an output is not meaningfully different from one based on a true RNG, but can be trivially fingerprinted by someone who knows the keys.

In practice, I am doubtful they have a scheme that is both practically useful and cryptographically secure. However, there is a lot of room below cryptographically secure that is still just as good for all other purposes.