Like Jno, I've never heard of a 'consolidation discharge' in relation to criminal law. Googling the phrase doesn't help either. It seems to refer solely to financial matters; I can find no reference to it being used, in any country, in relation to criminal law.
If your friend holds a passport from a country which would (if he didn't have criminal convictions) entitle him to use the Visa Waiver Program, he would be well advised to 'forget' his convictions and enter under the VWP. Otherwise, he'll have to apply for a visa. The application process (in the UK) typically takes around 5 or 6 months and involves both expense and inconvenience.
The US immigration authorities don't have direct access to the criminal records of any other countries (except for Canada). Unless he's suspected of cross-border crime (such as drug-trafficking, terrorism or sex tourism), the US authorities won't know anything about him.
Chris