Won't always work, though I can't prove how far off it'll be. Mainly, it should work pretty well when you have lots of extra space, but an approximate solution won't be "close enough" if you end up too close to exactly filling all the discs. Consider files of size 350, 349, 233, 232, and 231. You can fit them on 2 700 Mb discs (350+349, 233+232+231), but your algorithm will use 3 dics. (If you tried to use only 2, you'd end up with 350+233, 349+232, and the 231 wouldn't fit on either).
What I can't prove without a lot more thought is whether you're ever going to be off by more than a single disc, and what can't be proven at all is whether that's close enough for real world purposes. (Since what's "acceptable" in the real world has to do with how long you're willing to wait for an answer vs. how much you care about that extra disc, and other factors.) But just know that the greedy approach won't only be suboptimal in theory, but it will also, sometimes, bleed over into an actual difference.