You gotta unwrap it and get the cavity cleaned out. The giblets/neck/etc. will keep the inside real cold.
I just did a 20# pounder Thursday. Bought it Saturday and kept in a cooler with a couple of ice bags and a 10# bird for frying. It's the same as using the fridge but I didn't have room in my meat fridge.
Anyway, I kept it refrigerated until Wednesday night when I cut off the plastic, cut the leg restraints, ran cold water into the cavity and neck to make sure the giblet bag and neck came out along with any ice chunks. I made sure the joints were moving to prove it was actually getting thawed. I then put back in the cooler with ice bottles to keep until Thursday morning when I roasted the 20 pounder. I did the same routine with the 10# turkey but injected it with creole butter and rubbed with cajun spice in preparation for frying.
This is pretty much my routine all the time with turkey. That cook immediately crap will almost guarantee you a raw bird at the center. You gotta open that cavity up.
Your mileage may vary! Keep the bird cook and you'll be fine.