Hi Maulkin,
I don't think the flying school will have a problem with you turning up, explaining your situation and having an instructor sit with you while you fly around. But, this would be far from productive for your flight training as airspace and regulation in the US can be vastly different in areas and i'm not sure learning the US way would help your UK training. None of your US dual would be of any use back in the UK anyway if the school hasn't got the facility to teach JAR/EASA.