FWIW, I have been able to negotiate this option before -- albeit on UA, not DL. An accommodating GA was willing to do this on an afternoon bump from the west coast (i.e. reroute to a different East Coast city, overnight at UA expense, then take an early a.m. flight to my destination), even though there were seats on the redeye, and it was my preference to rule it out.

One caution, however, is that the hotel voucher could only be printed at the airport where I was overnighting, not at the airport where I took the bump. So that cut into my sleep time when I arrived. Also bear in mind that some of the MSP airport-area hotels are a longish shuttle ride or have no shuttle -- I think the nearest Starwood property is 5 or 6 miles away, for example.