The East of Scotland League club have been issued with a notice of complaint from the SFA's compliance officer alleging breaches of two rules.
The Edinburgh club were drawn at home to Partick Thistle in the third round, but they will be automatically thrown out of the competition if found guilty at a hearing on November 10.
That would leave North Region Junior side Culter with a plum home tie against Jackie McNamara's Jags.
THIRD ROUND DRAW
Culter or Spartans v Partick Thistle, Ayr United v Montrose, Irvine Meadow v Livingston, Stirling Albion v Dundee, Stenhousemuir v Alloa/Annan, Morton v Deveronvale, Airdrie United v Gala Fairydean, Keith v Arbroath, Fraserburgh/Elgin City v Queen's Park, Stranraer v Forfar, Clachnacuddin/Inverurie Loco Works v Peterhead, Ross County v Albion Rovers, Bo'ness Utd v Cowdenbeath, Auchinleck Talbot v Vale of Leithen, Brechin City v Dumbarton, East Fife v East Stirling/Buckie Thistle.
Ties to be played on weekend of November 19 and 20.