Erroneously failing to pay is not fraud. You say they have added costs so almost certainly they have been to Court & got a Liability Order. What will happen if they can't trace you is down to their policy. Some creditors will pass such things to tracing agents, & if they find out which country the debtor is in they will sell the debt on to a firm in that country - which will then pursue the debtor (& often the law is less favourable to debtors than it is in this country).
Of course, none of this may happen to you, but you are taking a chance & it may come back & bite you with a much larger sum.
Contact the Council & update them on your situation. Give them your USA address & confirm you will start paying as soon as you have a job & funds. But only do this if you mean it & actually carry it out.
And incidentally, Council Tax is one of the few debts for which you can be imprisoned so if you do nothing they may well at some point get an arrest warrant.