You'd be surprised at how tolerant a PCB can be. It doesn't do them any good, but I reckon it'll work perfectly.
Take it out before trying it, though, and bend the outer case back to as it should be - that way you don't risk a short between the case and the board.
And, of course, let us know how you get on!
(Incidentally, for that to happen when the shipper really has packed it properly, I'd expect the bottom of the box to be absolutely destroyed. To bend like that would have taken a lot of force, and if it had sufficient bubble wrap around it it would have had to puncture the box. When I ship something like this I usually try and put several inches of bubble wrap (probably 3-4 layers) and then some inches of packing peanuts. If the box wasn't damaged it was almost certainly either like that before it was shipped, or it wasn't packed well enough).