This is most likely civil law, not criminal. Criminal copyright infringement is harder to prove and generally has to be on a larger scale and for profit, depending on laws in your country.

Is admitting to breaking a license agreement enough for a conviction if you say exactly which license, then probably, depending on circumstances and specific local laws. Is it enough if you just say you did it, no. The licenser needs to at least prove they were the ones you "harmed" or they have no standing to sue. But if they already have logs from your ISP, then it might still be useful evidence.