Can you adopt with criminal record?

Here is the brief rundown of what happened: my now husband dated a woman on and off for about 7 years. They broke up in 1997 after they stopped getting along. Sometime after this, he heard from coworkers that she filed a restraining order against him. Since here had been no domestic violence or abuse of any kind, he wasn't sure why she had done this. Stupidly, he called her to find out what had happened. She notified the police and he received notice to appear in court. He pled guilty in court, since he had contacted her. He was fined and required to get weekly counseling. He was unable to afford the counseling and had to stop going. Because of that, a warrant was put out for his arrest. He was arrested in 2002 after a traffic stop showed the warrant. What shows up on his criminal check is a domestic violence court order violation, not classified. Doesn't show up as a misdemeanor. I have absolutely no doubt that this was a misunderstanding and a bad decision on his part to contact her, and I can tell you that this is not in any way what I know of him after 6.5 years. Even though I know this, will an agency?