Shock absorbers are designed to be installed in the direction presented in their owner's information. Their internal valving design determines how it should be mounted. This internal actuation is very critical to performance and mounting in the wrong direction will certainly inhibit their operation.
Some can mount "upside down", most should not be mounted in an inverted format. The shocks seen in many performance applications that appear to be inverted, are actually mounted in their proper orientation based upon design.