After thawing a turkey with the cold water method, is it safe to then put it in the fridge until cooking?

I put my turkey in the fridge to thaw it and realized it was hardly thawed out at all. So, I started the cold water method (cover it with cold tap water, changing it every 30 minutes, 30 minutes per pound). It's been out an hour and the outside is starting to feel thawed already. I allowed 8 hours for it to thaw, but I didn't take into consideration the couple days it was in the fridge thawing. If it thaws completely before I'm ready to cook it, is it safe to then put it into the fridge until then? I know the outside of the turkey thaws first and the entire cavity's probably a big block of ice that has to thaw, too, so maybe it will still take 8 hours, but IF it doesn't, I need to know if it's ok to stick it back in the fridge.