OK, yest it WANTS to flow back to 12V return, however the nature of electrostatic fields means this may not happen.
BTW, its UK mains sockets.
Lets say I point this HV output towards a metallic object, or just up into the air while its creating a corona discharge. Ions will fly off and eventually ground themselves on something nearby. Now the place they find ground, may have no return path to the 12V return of the PSU. Therefore as this process continues, the 12V supply gets increasingly charged to an opposite voltage to the HV output up to the point something will breakdown and it will forcibly find a return path to earth. I can even hear this happening inside the adaptor as little sparks must be tracking over something, presumably reaching the mains neutral wire.
I want to connect the 12V return rail (which is also HV return) to earth via a 1M resistor as it allows these 'lost' charges to trickle back up to the supply and keep all the low voltage electronics at ground level. It's not really being used to carry current as such, but is to prevent it from becoming electrostatically charged.