The offence would seem to fall into the category of 'moral turpitude' which, under the terms of the US Immigration and Nationality Act, automatically places a lifetime ban on your boyfriend entering the USA. So, in the first instance, the US Embassy MUST refuse him a visa. (Embassy staff have no discretion in the matter; it's their law).
However they could then forward the application to Washington as an application for a 'waiver of permanent ineligibility' to enter the USA. If that waiver is granted, the application can then be reconsidered. The process is extremely lengthy. (It typically takes around 5 or 6 months but I've seen a report, on this site, from someone who waited 15 months before being told that no 'waiver of permanent ineligibility' could be given, so he couldn't have a visa. He had two convictions for driving without insurance). With such a recent conviction, it's probably extremely unlikely that a waiver (and hence a visa) would be granted.
That leaves him with having to 'chance it' by 'forgetting' about his conviction and attempting to enter the USA under the Visa Waiver Program (with an 'ESTA'). The US authorities have no direct access to UK criminal records and many people seem to have got in under the Visa Waiver Program, without any problems. However the UK will make criminal records known to the US immigration service if they receive a specific request for information about any particular individual. Because security matters are shrouded in secrecy, nobody knows just how such requests are made, but there have been quite a few people who've been turned back on arrival in the USA because they'd failed to declare criminal convictions.
There can be no definitive answer to your question. I'd regard a visa application as unlikely to succeed but nobody can guarantee that 'chancing it' will succeed either.
Chris