The answer would depend on whether the judgment creditor had extended credit to the debtor--without having extended credit, the answer is presumptively no.
However if there was no credit extended, authorization to view the debtor's credit report on an as-needed basis is something a court should easily grant, and a sensible debtor will stipulate to it rather than making a judgment creditor bring a motion before the judge.
Yes, a judgment creditor can get a credit report. Also, a judgment creditor can get a court order for the debtor to appear in court and bring with you any credit reports that you have and all your bank records and other financial documents, so they know where you have any money and where you work so they can garnish any wages, to the extent permitted by law. The judgment is also most likely to appear on your credit report for many years.
This is yet another reason to take these lawsuits very seriously and either get them settled when you are served (see my Avvo legal guide on how to settle a debt collection lawsuit) or hire experienced debt collection defense counsel to defend the case properly so that a judgment does not result.