This is a grey area which has never had a definitive answer, only rumour and could possibly be better left that way and not bothering a CAA offical over. Hate for them to make a negative ruling!!!
The problem in the past stemed from guys doing the flying without a type rating and then claiming it as P1.
Under US regulations, either PPL or CPL a type isn't required but CAA/JAA does require one.
In your situation you have a JAA type rating for a 206 and a US PPL(H), plus will fly the aircraft with controls in YOUR hands, so you can log it as P1 on either licence, regardless of which seat you sit in.
Can't personally see the point in doing over 100 hours though, as on your return to the UK it is fairly well known that this is little more than an hour builder and won't put you in any superior position in a job hunt than someone with a bare CPL(H). Can't exactly put 'employer' LA trafficwatch on your resume to cover the hours!!!
In my humble opinion your money would be better spent on hunting for your first position.