Joe sure did according to some.
Like you, I think if a food source is tied with blocks and tossed in the river a gator may 'store' the food source if not eaten right away.
I found these items and snipped some:
http://plants.ifas.ufl.edu/guide/alligators.html
From the link:
Feeding activity is determined by water temperature. Temperatures below 68-73 degrees Fahrenheit will curb an alligator's appetite. In North Florida, alligators enter a period of dormancy during the winter months and reside within excavated caves along the water bank. In southern Florida, alligators are active hunters all year.
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http://www.american-alligator.com/Diet.html
From the link:
In the summer, alligators eat lots of food and build up plenty of fat on their bodies. When the weather grows cool, they eat much less. They can go without food for weeks in the winter.
Both links indicate they "eat less" or "curb appetite".
Not "never eat" in winter.