What it will primarily come down to how the debts that are included in the debt management plan are reporting to your credit.
In a debt management plan sometimes they all report on time, sometimes they all report late, sometimes it's a mix of late & on time. So if you have some that are going to report late all the way up until the plan is complete, you could have some problems when it comes to underwriting if you want to buy right afterwards. However if they are all reporting on time then the fact that you were on a debt management plan probably wouldn't even come up.
In the situation where some/all would report late until the plan is complete, if you have made all of your plan's payments on time and the management company would be able to verify as such, then it would likely be acceptable if you chose to go with FHA financing.
670 scores are fine to qualify for both FHA & conventional financing (with conventional you may need at least 10% down with that score though), but if there are late payments reporting during the management plan then it may be tough to qualify for conventional so soon afterwards.
You may be surprised to know that it's even possible to qualify for financing while you are still in a debt management plan, probably not advisable if someone is trying to dig themselves out of debt, but it's possible.