Powering 12V LED strip thru European hinges
Yes, it's been done. For instance some GM cars supplied power to their rear hatch defogger through the hatchback lift springs (you know, that look like shock absorbers and help you lift the hatch). 

However hinges are not made or listed to carry current, so you may run into trouble with poor contact and arcing at the hinge.  

The right way to do that thing is to put a jumper strap across the hinge, made of a highly flexible braided wire made for thousands of flex cycles.