It would depend upon the nature of the debt and which courts were invoolved.
If it related to unpaid fines (or unpaid costs of a trial in a criminal court) then it might well come to the attention of any criminal court that the debtor appeared before.
However criminal courts would not be interested in civil matters (such as unpaid costs from civil courts or defaults on CCJs).
A civil court would only regard a court order for debt (made elsewhere) as relevant if it related directly to the matter before the court.
Chris