From my experience, even as a DM DL will make you wait an extra day, two, three or four before having you fly out (status appears to be meaningless with DL in irrop situations). DL has categorically refused to rebook pax even on SkyTeam airlines like KLM in such situations before, when it's aircraft goes mechanical and next flight out isn't for two days later. (DL has by far the worst irrops handling of any major airline, as DL is very cheap. It will rather delay you by not just one but a few days than ticket you on another SkyTeam airline, even with wide open availability. DL may insist on original routing and that there can be no deviations on it. I mean helpful res agents will get you put on alternate routing and flights, but DL just will not budge and won't ticket it.)

So, basically you will be on your own and expect to pay for your own alternate flights out, and then fight with DL for compensation.

If this is something you are concerned about and getting from A to B on time is important and you don't have a few days +/- flexibility, don't fly DL. Book any other airline.