Unfortunately, no one here is going to be able to give you a definitive answer to this question.
At this time there is serious doubt rather we'll get any DLC at all. If we do, there is no way for us to know what it would possibly contain or how it would work with the main game.
Generally though, you should be fine. If you start a NG+ that should be a different save entirely. If they did release DLC and you didn't complete something on your NG+ run, you could either just complete that task before doing the DLC, or load your original run and complete the DLC with that character.
A lot of us are hoping that EA will decide to update the community on that status of Mass Effect Andromeda DLC but sadly so far our requests have been met with silence.