The theory of the dry ice is based in science. In practice it really is about the alloy , and the actual dynamics of the dent. Most often, I wouldnt expect dry ice to work. I have seen it demonstrated on youtube, but those videos basically show it working on something like if someone sat on roof or hood or something, that you could easily pop out by hand too.
If it is going to work it has to be within a day or two of the damage. You need to be able to shock the temperature of the metal ( you may need to gently heat/warm before you apply the ice ) I think this work on larger dents rather than small ones. But used in combination with some paintless ding removal techniques, you may get some some surprising results on a select few.