I'm not sure whether status makes a difference, but DM and SC agents have always told me that I would be taken care of if there were IROPs problems on separate (DL to DL) tickets. They certainly did at the time of the August (what year was it?) worldwide meltdown supposedly caused by electrical problems at ATL.

OTOH, when I'm doing this with a cheap D1 ticket, I try to fly to the airport where the second ticket starts the day before especially if I think there could be risky weather. It's usually also a way to collect a cheap Hyatt night at an OK airport hotel for requalification. I also prefer the overnight connection with an airport hotel along the way to a very early connecting flight when I have time to do this.