This is a common concern, and the answer is more nuanced than most sources let on.
Just getting counseling: Having a free counseling session has zero impact on your mortgage application. It doesn't show up on your credit report. No lender will ever know unless you tell them.
Enrolling in a DMP: A DMP may appear as a notation on your credit report (something like "account managed by a credit counseling agency"). This notation is not a negative mark, but it is visible to mortgage lenders.
How lenders react varies. For FHA loans, HUD guidelines specifically state that participation in a credit counseling program should not be viewed negatively. In fact, it can be seen as a positive indicator that you're managing your debt responsibly. For conventional loans, the response depends on the lender and the underwriter. Some don't care at all. Others may ask questions about why you're in a DMP.
The practical impact on mortgage approval depends more on your overall financial picture than the DMP notation specifically. If you're in a DMP, making all payments on time, and your debt-to-income ratio is improving, most lenders will view that favorably. What they care about is: can you afford the mortgage payment? Is your debt trending in the right direction? Are you managing your finances responsibly?
Timing matters: If you're planning to buy a home in the next 12 months, enrolling in a DMP now might complicate things because your credit cards will be closed (reducing available credit) and the DMP payment adds to your monthly obligations. If homeownership is 2 to 3 years away, a DMP that eliminates your credit card debt before you apply will actually strengthen your mortgage application significantly.
The alternative perspective: If you have $20,000 in credit card debt and you're trying to qualify for a mortgage, that debt is already hurting your application. A DMP that eliminates it, even with the closed-account notation, puts you in a better position than carrying the full balances at 24% interest.
Talk to a mortgage lender (not just a credit counselor) about your specific timeline and situation before deciding.