Joe, I think you hit the nail on the head with this:
I would guess that if they are hungry enough, they'll still eat.
Personally, I have never used any of the liquids. I have met people who claim they work great.
And I have met those who tell me that the liquids are useless.
If you have lush, green fields, and it is dry and barren beyond your fence, I don't believe anything would keep them away. By the same token, I know people who have spread nice seed mixtures beyond their fences, and seldom see the deer on the inside of the fence...they are provided with plenty of food outside.
Worst comes to worst, you need a bigger freezer.