Lets just clarify a few things.
In the eyes of US immigration you have a class A drug conviction and any drug conviction is a big no no to US immigration - especially class A's. I can pretty much guarrentee you will be denied a visa. Best case scenario is the consular official recommends a waiver of ineligibily. Perhaps because the conviction was some time ago - this will be sent to the homeland security for evaluation.
Secondly I doubt you answered the ESTA questions honestly as you suggest. If you had answered Yes to the questions about Crimes involving Moral Turpitude then you most likely would have been told to apply for a visa. A drug offence is a Crime involving Moral Turpitude.
Thirdly US immigration DO NOT have direct access to the PNC but what they do have is an agreement with their UK counterparts to share information. Therefore you fill out ESTA and they have 72 hours to ask the UK for information about you. You won't know until you arrive at the Port of Entry if you've been lucky to get through the net.
And finally the primary reason for taking the prints at Port of Entry is to ensure that you are who you say you are. ie you were Mahommad last time and now your Dave.
The risk is all yours not only for this trip but all future trips - best of luck.