Taking the twist out of the bed has to be one of the first priorities. (Work can be turned parallel, if the the Tailstockm is misaligned, but unused ) Seeking accuracy has to be undertaken, when the basics are correct, (No excess wear in the bearings, bed or Saddle, loose gibs, and so on. )
Since the lathe can turn a cantilevered workpiece parallel, aligning the Tailstock across the bed will only help to ensure parallel turning between centres.
NOW we get back into the argument about how great is the effect of vertical misalignment. The last time this argument took place, it seemed that vertical misalignment had a far smaller effect than horizontal..
It is all a matter of priorities. No good worrying about how deep a cut can be taken, how accurate the machine is, or how parallel it will cut, if the motor won't run!
Howard