You can use the outside of the electrical conduit provided the conduit has a continuous reliable electrical connection to earth ground.
Ground wire in attic.
Strip away about 6 inches of outer insulation and 1 2 inch of individual insulation from the end of each wire.
Check to ensure that the vent tube is firmly grounded before connecting the wire.
How to run wire through an attic step 1.
I found that a firm grounding of antenna mast gave a better reception as well.
Lets you do precisely what you are describing running a separate ground wire to an existing point on the equipment grounding system originating from the same panel.
Bare copper antenna wire stapled directly on wood rafters causes loss of rf signal energy.
With time bare copper oxidizes the wood where the wire is tightly stapled to absorbs some of this oxidization and forms a loose yet lossy bond with the wire.
This is usually a moveable piece of drywall or plywood that covers a rectangular hole in.
Use wire nuts to connect.
Insert the end of the 12 2 wire into the fans junction box.
Air movement in your attic should not pose a problem.
Measure the distance between the two sites you want to run wire between and make sure you will have enough wire.
The copper wire at the base of the antenna mast attaches to the copper vent tube that runs to the roof through the attic in a 55 year old house.
You have to inspect it along its full length until you reach a working ground wire.
Find your attic access.