Not all criminal background checks are the same. Many, if not most, checks focus solely on convictions. Indeed, some look only at felony convictions. Others, however, are as thorough as a FBI check, reviewing all criminal charges for which available records are available irrespective of their resolution.
In short, your bf should not allow the prospect of this charge being discovered to hinder his search. It may not be a factor in a background check at all. Moreover, if he asked about the underlying incident, he should tell the truth. IMHO, it is likely not a deal-breaker for a prospective employer interested in hiring him.