Not unless the conviction was for an offence where the UK authorities had 'justifiable cause' for revealing details of the conviction to the US authorities.
EU law bars the UK from opening up UK criminal records (including fingerprint records) to overseas authorities unless there is specific' justifiable cause'. That normally refers to convictions for (or suspicions about the possibility of) terrorism or 'cross-border' crimes, such as drug-smuggling, child-sex tourism or people-trafficking.
Chris