GDPR doesn't just cover personal info, it also forbids tracking without consent, which includes cookies and other means. This is just a technical trick to track someone sans cookie, so I'm 100% certain they will fine anyone doing it unless they get consent.
The GDPR is entirely about personal data stored by the processor [0]. In principle, if the tracking is entirely client-side, and never produces any traces in how the client accesses your server, then the GDPR alone has no ability to stop it. (Not to say that it cannot run afoul of other regulations.) If the results of the tracking are somehow sent back to your server, then it most likely becomes personal data subject to the GDPR.