I was thinking in particular about Brie because of its soft texture...
We've successfully frozen shredded mozzarella and then baked with it without losing flavor. Apparently the thing to be concerned about is the texture, not the flavor, and harder cheeses tend to retain their texture better (though using them for cooking/baking is still the only recommended way) according to Still Tasty.
Brie will probably freeze well since it doesn't have a curd structure and is fairly high in fat. I imagine the flavor won't be quite the same, but it should still be close.
In my youth, before you could buy good cheese at supermarkets, my mom used to buy huge blocks of cheese and freeze them in a chest freezer. The flavor was about the same, but they were a bit worse for the wear. With cheddar, the curds would become much more pronounced for some reason and the cheese would appear drier than normal. I think the freezing shuffles the water around somehow in the curd, but I'm not sure.
Parmesan always did fine, with no observable difference between the frozen and raw product. I assume this is because it has a very low moisture content.
Try it out with a bit of cheese and see if the thawed product is passable.
I have frozen Brie, having found it on clearance at the store but not having a plan to use it any time soon. Once defrosted, it seemed (to me) to be the same as if it were fresh.
I have frozen a variety of cheeses. The tastes seem to be just fine, but the texture is definitely different. Cheddar tends to crumble and mozzarella seems a bit drier. I prefer to shred then freeze, as I'm more likely to use it shredded than whole anyway.