There is no hard and fast rule but I've had many years selling thousands of flights to USA. My agencies were mainly in poorer suburbs where many young people were unemployed and/or had minor convictions
Many more had no convictions but had been arrested but then released or gone to trial and been found not innocent.
Unless the application form for a visa (and everyone needs a visa to USA even though the Yanks pretend that the ESTA form is not a visa) has changed in thr last year, it asks whether one has been convicted or ARRESTED for any offence. I forget the phrasing on Aus visas.
By far the biggest percent of refusals were from the USA -and I'm sorry to tell you that these were for young people who had committed quite minor offences. How "minor" your son's offences would be considered I don't know.
In most cases of refusal in the last few years the applicant was directed to the US consulate in Dublin for an "interview" and - guessing from memory - about half the applicants then got their visas/ESTAs.
I always wondered whether those who were refused were refused because they looked "rougher", had no real credible documentatioin proving income, steady job in ireland and the other factors that US immigration officers require. In other words the conviction may have brought them for an interview,but other negative factors may have influenced the interviewer.
Over the years I got to know my regular customers and often came across a problem with -for example - their 20-something year old son' getting the ESTA/visa - even when travelling with parents on a family trip. The son may have had(usually)a minor drug conviction a couple of years back, petty theft, shoplifting (that was usually the girls) etc.
In order to help them I'd write a letter saying that had booked and paid accommodation,return flights -were regular clients etc etc. They also got letters form employers, priests etc etc.
I repeat -I don't know how your son's offence would be regarded but -yes, strictly speaking -he should put down the details on his application and expect to go through the above hassle.
Whether he does put down the details or not is up to him. With the increase in internet surveillance one always wonders whether every last details of somebody's life finds it's way to the US authorities (one should ask Mr Snowden this!).
Of course if somone has a problem and his name is Kelly it's quite easy to get a new passport in the name of,say, O'Ceallaigh.
Except for nthose applying for a Australian work visa I can't recall any such similar problems.
Fianlly, I think all such convistions for minor offences are wiped off any criminal records after a number of years. (Though maybe not from the USA's!)
Sorry for this gloomy waffle -it's just that your question brought back many memories of young people who had hassle getting into USA because of mishaps years previously, and I know it's not what you had hoped to read.
sorry i keep saying your son. My mistake