I was always taught the Vortex Ring State can be eliminated if you push forward on the stick, would this also work if you went Left or Right?
Yep.
In true VRS the A/C will briefly be sinking at an alarming and accerarating rate in its own cocoon of air, which is recirculating around the M/R blades.
That is of course until it sinks fast enough to have the onrushing relative airflow simply blow the cocoon away as it accelerates downward.
If you would like to load your A/C laterally heavy one way, establish VRS, hold the cyclic central, and watch the aircraft FALL toward the heavy lateral load, it will simply come out of VRS in that direction.
Or, if the A/C is loaded level in a lateral sense then you can fly it out in any direction that you choose as per the standard recovery technique.
But don't try that at the bottom of a downwind auto, as by the time you mess around with that then the real ground effect, which is the crump at the sudden arrival, will have caught you.
In auto, if in doubt as anywhere, always shoot with cyclic toward the A/C inertia. (that's the direction the A/C is travelling in)