Why not log the time?
Example...I run into a guy that has a DC-3 that he uses to haul herbal leafy material from sunny climes in Central/South America to Florida. I have no pilots license at all...zip, nada, nothing. However, I am a very clever fellow and decide to fly the Goon for him.
Over time I accumulate a load of cash....skin cancer... and a criminal record...donate all my hard earned cash to the Federal government in exchange for forty years free accomdation at a Club Fed somewhere.
During the flying portion of that career, I build 2,000 hours total time, 300 hours IFR, 1500 hours night, 1800 hours cross country, and 1975 hours PIC, 25 hours Dual and 1975 hours Solo.
What prevents me from "logging" every bit of it....after all I flew the Goon single pilot didn't I.
The FAA says I can log it...but I cannot use any of that time towards a certificate(license) or rating. They might consider taking action against me but I could still log the time.
What the CAA would say about the situation the original poster would be an all together different matter.