I was an adult probation officer, and contrary to what people might expect, I liked most of the folks I worked with. They were moslty surprisingly normal people who made a single or a lifetime of bad choices. There's often no way to tell on the outside, whether the person was one-time stupid, or chronically stupid, but there are clues (and the clues here, tend to point towards chronically stupid).
Assuming he's telling the truth, and all of the offenses are non-violent, it'as actually a worse sign (to me) because in most, if not all states, to be thrown into prison for failure to pay child support you've got to be negligent for YEARS before it would reach the incarceration point.
By the way, there's a big distinction between jail (incarceration in a local jail, run by the sheriff's department generally for no more than a year and a day) and prison (tends to be longer than a year, but can be as little as a few months, offenses are more severe).
Personally, I've never seen anyone sent to prison for child support. Jail, yes, but not prison. I'm not saying it can't happen, I know it can - it just makes me really suspicious that there is more to the offense than he is saying.
When I was in my 20's, I once placed a penpal ad in a penpal magazine (luckily to a PO Box). It was a lady's crochet magazine and it never dawned on me that it would be a popular magazine in prisons - but prisoners are desperate for outside world contact. I got so many prison letters (and the return address wouldn't even hint that it was from a prison, so if I hadn't been tipped off by the writer, I would never have known - and some guys didn't say they were in prison, I only recognized the address on the letter from someone else admitting they were in prison). I never answered any of the prison letters, but I can tell you that not one of the dozens I received admitted to being incarcerated for a violent offense.
I'm not sure your friend is going to listen to anything you say. Ideally, she would go to her local sheriff's department, express her concern about a guy she's wanting to date (NOT telling them he's already in prison) and asking if they would do a background check for her (she may have to pay a fee, usually around $20, possibly more, but a good investment, nonetheless).
My husband was in HR in a field that attracted folks desperate for a job. He has a saying "trust, but verify." Many folks fear that verifying information proves that you don't "trust" the person, so they don't want to do any checking because it "proves" they mistrust the person. That's just silly reasoning, the fact is that liars aren't really very successful if they can't convince you they are telling the truth. As a result, you have no way to tell if anyone is lying, except through verification.
If I were her, I would ask him for contact information to speak with his ex-wife to get her side of the story (allthough I'd that with any divorced man I was wanting to date, even without a criminal record - and I'd always do a background check on anyone I dated).
To be honest, all of the work it would take to screen an incarcerated man, I'm not sure it would be worth the effort to me, but I'm afraid your friend may not be willing to hear much of this.
I met my husband through a personal ad I placed, and I went in suspicious, assuming that everything he said was colored by his desire to make a romantic connection. I did have a background check done, both in WI and in IL (not even a traffic ticket). It's an easy enough precaution to take, that I think everyone should do it. You've also got to assume that for every conviction, there were five to ten times as many times he was lucky and just didn't get caught.
I'm not sure your friend is willing to be smart about this, but you can be. If she won't do the background checks, I'd suggest that you do. I'm assuming that as your friend, you will have contact with them as a couple. If she isn't willing to protect herself, there's no reason that you shouldn't.

