I think that is exactly right. It also depends on where the deer dies. If it is shade or in direct sunlight, or if it is in the bottom of a dark revine.

I would still suggest getting out therein the morning though, but not before good morning light. From the decription of the arrow, I'd have to say the deer is probably dead but may be up to 12-15 hours from the hit. Good luck, and let us know please.