Jon,
The part that you described is properly called the Arbor Driver. Although many of the Atlas mills turn up without one, I wouldn't try to operate the mill with the arbor without it. If the taper shank ever spins in the spindle, you won't like the consequences.
Like the chuck on many an Atlas lathe, PO's often went decades between removing (or trying to remove) the arbor driver. This actually falls under the "operator head-space" category. But unfortunately, Atlas didn't bother to caution against doing this in any of their literature. Although the arbor driver is mentioned in the mill manuals, they never say how to remove it. The same is true of removing chucks in the lathe manuals. However, in the Manual of Lathe Operations (MOLO), the method given for removing a chuck from the spindle is to lock the back gears (engage them without pulling out the back gear pin). Then insert the chuck wrench in the chuck and pull smartly toward you. The MOLO doesn't say what to do if the first try fails to loosen the chuck. My SOP over 30 years has been to try it a second time, which has never failed to work. I'm sure that the same procedure will work for normal removal of the arbor driver.
However, if you buy a mill and it has the arbor driver screwed onto the spindle, I would treat is the same as a new to you lathe that arrives with a chuck installed, unless you know that the PO followed good practice of periodically removing either. In other words, treat it as stuck and use an alternate method to hold the spindle while you attempt to get the driver unstuck..
Another matter is that although Atlas supplied a tool for pulling out the back gear pin, they never to my knowledge supplied a spanner for removing the arbor driver. I would recommend that you make one from a 12" piece of 1/4" steel bar stock. Drill six equally spaced holes to fit the pins on the arbor driver pin circle diameter.