Moving soon but decided to start debt management, will I be able to rent a home?

It’s possible, and I would not expect the debt management itself to show on credit, but having credit to manage will. Some renters run credit checks and care about them, and others don’t. At least you weed out one flavor of asshole landlord if they turn you down based on a credit check. If you have past landlord references, they would hopefully be enough for a human landlord.

It might make a difference, but on the other hand, starting debt management shows financial responsibility, not the opposite. If it came up, the conversation should be about how you had gone the wrong way financially and are turning it around.