If the furnace is set up woth a direct whole house ventillation then u should be fine with just the house system running. If not im sire oxygen and fresh air get into the room someway somehow but to make sure u have fresh air coming in and old stale air going out is always a huge plus.
Without ventilation, a drying room needs fresh air intake to prevent odors and maintain oxygen levels. HVAC air circulation alone may not suffice, leading to potential issues like chlorophyll smell and oxygen depletion.