It depends. I'm in a DMP as well and I tried to several occasions to pay additional payments through online banking, and Crap1 and Citi would not let me. I could not change my address of phone number online with either of them either. Customer Service told me it was because I'm in DMP.
It may or may not affect the benefits you get through the DMP, but you'd have to call each creditor because they seem to all move differently. I would check with them first before I make any move.