Linear regulator GND pin MUST be connected to common ground?
Generally linear regulators can be used in various modes which are not quite as the original developer envisioned, including as current sources.

However, what the "third" pin does is rather less defined in some devices than others. When using it the way you indicate, you must remember there is a bias current that emanates from the "ground" pin. Basically the quiescent Icc of the device.

This bias current will of course be driven through the load in addition to whatever you have set your regulator circuit to produce. You must therefore compensate your values to take that into account. How much ambient current that is will depend on a the device and a number of variables that may or may not be well specified, or even controlled in the device itself. 

Furthermore, if the load is a fixed load, using a voltage regulator may work for you, however, I'd be cautious if the load varies, or is switched on and off, since this will also affect the bias point of the regulator and it may become quite unpredictable.