TL;DR: Yes, automation has progressed in the ED universe to a point where the largest playable ships could conceivably be crewed by a single person.
Longer answer:
The largest playable ships in ED are comparable in the size to modern destroyers, which are typically ~160m long. By volume, these ships have about half of the internal volume of an Anaconda, which in turn has about half of the internal volume of a Corvette or Beluga. We can therefore assume that number of people needed to crew the largest playable ships in ED without automation does not exceed the number of people needed to crew 3-4 modern guided missile destroyers. Note that this figure is a high-end estimate.
A Farragut battlecruiser is a little over 2km long, 800m wide, 300m tall, and needs a crew of 7000. For reference, a Nimitz-class aircraft carrier needs a crew of around 6000 (including the air wing). If you calculate the size difference between the ships, the Farragut comes out as being about 400 times larger than a Nimitz (by volume) while only needing a 17% larger crew. This means that automation in ED has progressed to a point where a single crew member with the help of automation can perform the tasks of about 340 crew working on a modern ship.
Considering that most guided missile destroyers and multi-role frigates have a crew complement of around 250-300, it is entirely reasonable that something like an Anaconda could be operated by a crew of 1 or 2 individuals, and that a Corvette or Beluga would only need a crew of 2 or 3
Of course, only needing a crew of 2 or 3 does not mean that you couldn't have a larger crew to allow the ship to perform a wider variety of tasks. We already have NPC crew that we can hire to fly SLFs, this feature could be expanded to include NPC gunners, engineers, quartermasters, flight attendants, sensor operators, etc..., it's really just a question of having the gameplay to support it.