NO. Your Executor has an obligation to repay all debts from your estate first, before doing anything else.
Having said that, if there is little money left in an estate, than most debts can't be paid after death. Its unlikely that most creditors will press very hard for monies.
If you have no assets to discharge your debts, they cannot be discharged (and strangely the funeral account counts as a pre death liability). However, joint property (whether real or personal) can be clawed back in order to discharge debts.