I can tell you with certainty from using Palm phones and the Touchstone in the past that it depends on the thickness and material of the case. You're not going to be able to get one blanket answer for this.
Yeah seems like the charging has about a 1" range or slightly less so unless the case is metal perhaps (not sure if that would screw with the induction, but I imagine it might) a rubber/plastic type case should be fine.
Instead of a case in the general sense which it wraps around the back, why not a screen protector / case that wraps around the front? It would offer anti-glare properties or even a privacy screen which gives the Lumia a bit of cushion should it be, I don't know, dropped two feet above the ground as some poor guy is trying to climb out of his Honda Civic.