Generating plausible private keys isn't that trivial. They are derived in a specific process from a part of the public key, and this process involves double hashing.

If by "plausible" you understand correct from a formal point of view (length, allowed chars), this is of course trivial. It's like you would say a person has one nose and two eyes (to continue our GAN example).

But if by "plausible" you understand "with a higher probability to find a fit in a specific set of public keys", then it's different and it's my understanding that GANs can help here. They may create something very close to that, in the same sense they are creating very plausible faces, not just sketchy noses and eyes (have a look at that site).

A very simple explanation of a GAN is that the forger learns specific patterns (nose, eyes, hairlines) by approximating the distance in pixels from them (it's way more complicated than that, obviously). In this sense, if there are patterns in the cryptography generating process, or recognizable groups of letters, etc, a GAN can be closer to a public key than just brute-brute force.