Almost certainly not as described by Derek de Solla Price in his key publication “Gears from the Greeks:
‘Only six divers were available and because of the water depth they could not remain on the bottom for more than five minutes, which together with four minutes for ascent and descent entailed about nine minutes of submersion without air-tanks or tubes to help them…’
But by divers using closed, flexible diving suits, with copper diving helmets and surface supplied air.
The ‘diving helmet’ was invented by Charles Anthony Deane in 1823, and the first workable SCUBA by William James in 1825. However, Augustus Siebe, who (in 1837) attached Deane’s helmet to a closed diving suit, is often regarded as the father of diving. As an indication of how advanced diving technology was, in 1843 the British Royal Navy set up the world’s first diving school, after several successful underwater salvage and demolitions.
By late the 1870’s the Greek sponge divers had fully adopted the diving suit, and almost certainly the sponge divers who discovered, and those who subsequently worked on the Antikythera Wreck would have used a diving suit and helmet, with an air hose attached to the surface.
In 1905 many Greek sponge divers were lured to Tarpon Springs, Florida and with their ‘advanced technology’ of flexible diving suits, copper helmets and surface-supplied air, the Greek divers consistently brought in more than four times as many sponges per man, per hour, than harvesters using long-handled ‘hooks’ or ‘rakes’ from the surface. Tarpon Springs was ultimately to become the sponge capital of the world.
Unfortunately, Price’s description of the recovery of the Mechanism by free-diving sponge divers still persists in even the most recent articles.