I bet that the 'shock' part of the front coilovers (which is what they are, coil springs over a shock, all as one assembly) is made to run right side up. There is oil in there and valves that respond to movement.
I say this knowing that most automotive shocks are not supposed to be run upside down. Some higher end ones that are rebuildable, like bilsteins, FOX, FOA, etc can be run upside down or whatever because of the way that they are built, but regular old shocks don't work well upside down.