Assuming the debt is legitimate, this does indeed constitute a delinquent account. However, this is a civil matter, not a criminal matter. This account would not constitute a criminal conviction or even a criminal act.
You would be aware had you been criminally convicted. You'd have been charged by a police officer and would have had to show up in court. That sort of thing doesn't happen to bad debts except in extreme circumstances. Obtained monies through fraud? Filed false tax returns? Then you may be criminally charged. But short of that, no.
Note that I have a guy who stiffed me out of about $12,000 for computer programming work I did for him. I filed a civil suit against him and won. Even then, he never paid up. But because this was a civil matter, he could still honestly swear he has never been convicted of a criminal act.
Off-topic, but note that pretty much every member of the population has committed a criminal act of some sort; it's almost impossible to avoid. You should be careful stating otherwise. Most forms would only ask if you've ever been convicted, or perhaps if you have ever been charged.