I'm not even sure it would take that long. Freezing organic matter causes water inside to crystalize, which destroys cell membranes and does pretty bad damage to whatever is being frozen. Of course, the longer the crystals are given to form, the worse the damage becomes. We call this phenomenon "freezer burn."

Have you ever taken a plastic bottle full of water and put it in the freezer? Unless you leave room in the bottle for the ice to expand, the bottle will break. This is pretty much what happens when a cell becomes frozen.

A month would certainly give the ice crystals plenty of time to pretty much eradicate anything living within the organism, but I'm willing to bet that few organisms would survive more than a few days after being frozen.

Please note: I am not a professional biologist. I just watch a lot of Good Eats with Alton Brown.