You can draft a doctor, from pool of doctors. You can't draft ATC, because there is no pool of spare ATCs. It would be like drafting air defense operators - there is no pool of them outside military.
I'm pretty sure some of the air traffic controllers for military airfields in WWII were draftees, just like many air defense operators were draftees before the military became an all-volunteer force in 1973.
If the recent news about moving lots of soldiers from EU Nato installations back home is true, they'll have a ton of trained active military ATC's available to use in the US soon.