I know this is done with fish, that they can be kept in ice water for a while until you dock the boat & have time to clean them. And when you hunt you can carry your ducks, turkeys & pheasants around for a while. My only concern would be if there was any poop left in the intestines & it leaked out into the ice water through a limp vent, and contaminated the meat.
Perhaps you could contact your county extension office for information. Meanwhile, go ahead & clean out the carcass as if it were edible (use rubber gloves, sterilize your cutting board & knives afterwards), rinse it out really well and use double bags to store it in the refrigerator. That may be more effort than is needed, but better safe than sick & sorry.
This is why I advise folks to not pre-kill more than one bird at a time. I will slice my first bird & hang it out to bleed while I'm catching up the second candidate. Then I slice & hang the second one while I pluck/skin & clean out the first one. And continue in that way until I'm finished. That way if something comes up to interrupt the processing process, darkness, bad weather, Publisher's Clearinghouse coming to my door with a million-dollar check, etc, I may only have one extra dead bird to do.