Those teeth on the inside of the capo look a little bit sharp...or pointy...
Depending upon the tension of the spring, I'd be worried that you'd end up with dimple-like impressions in both the back of the neck, as well as impressions on the strings, and neither would be good...
If there are dimples in the back of the neck when you remove the capo, you are likely going to feel that with your thumb when you fret notes, and then the back of the neck is basically damaged. you might be able to fix it, but feeling it would bug me...