This will work just fine. We did this last summer with no significant issues. Note that the DI will freeze almost anything solid - including beers which (as mentioned elsewhere on these threads) will split most cans.
Also mentioned elsewhere here, but setup your coolers so that the DI is on top of the stuff you want frozen, preferably near the top of the cooler. Capt. Obvious reminds you, "Colder air sinks". We kept cheap space blanket (reflective) on top of the DI and taped the cooler shut.