Enrolling in a debt management program usually implies a payment negotiation with the creditor to reduce the regular monthly payment on your loan to an amount established by the debt manager; an amount that will be commensurate to the budget they develop for you.
The effect of this on your credit is derogative. Any change to the agreed-upon terms of your loan (whether it be an installment credit or a revolving charge account) that accommodates a financially distressed borrower, even if the change is accomplished by a formal modification of your loan documents, will usually have a negative impact on your credit score.
If the monthly budget developed by the debt manager does not change the amount of your regular monthly payment to the creditor there should be no implication, negative or otherwise, and your credit should not suffer. However, this is rarely the case as contracted debt management is typically resorted to only when the debtor gets upside down in his/her budget (when expenses exceed income), requiring that each creditor take a smaller payment than originally agreed to.
However, in my experience I’ve seen that negotiating a reduced monthly payment with your creditors is usually not something a third-party contractor can do better than the owner of the account. And developing a monthly budget that works by reducing the amount paid to each creditor each month is probably better done first-hand (by the debtor) than by a third-party that is not fully vested in the financial consequences of the debt management program should it fail.