In nature in happens all the time its called "winter" , so if i reason it like that i can concluded my answer to be"yes" but i want to know from someone whos actually done it or has a reliable source to confirm weather or not you can get away with freezing ur fully colonized jars for a prolonged period not more than a few months or so ?
The mushroom mycelium will die when the temperature reaches 0 if you want to slow down growth use a fridge
In winter, in nature, I think only the spores survive.
Also, "in the wild" myc grows deep into the soil. The myc at the surface is killed off by the cold, but the strands that are deeper are not frozen. When it warms up, they reextend themselves up toward the heat. Nature finds a way. The clinical lab version, not so much.