Others have reported that they were not permitted to board the delayed flight, so I think that's an issue. EHAS states that it takes them up to 12 hours to approve your submission, so I would think you'd be safe to get your test on Sunday if your flight is on Tuesday. Even if you don't have everything in hand and printed before you drive to KC, you can still access your email and use the hotel's printer to print your paperwork. Were I in your position, that would be my plan.