Its worth noting that when first introduced by homer, Cerberus was not referred to as multi headed, or even as a dog. Some of the early authors don't make reference to many heads.
Aristophanes evens says in the frogs:
"O, villain, villain, arrant vilest villain!
Who seized our Cerberus by the throat , and fled,
And ran, and rushed, and bolted, haling of
The dog, my charge! "
But this may be dependant upon the translation. Cerberos and has variously been 50-headed (Hesiod, Theogony), had a snake tail (Pseudo-Apollodorus, Bibliotheca) or even had a mane of snakes:
Here the savage Stygian dog [Kerberos (Cerberus)] frightens the shades; tossing back and forth his triple heads, with huge bayings he guards the realm. Around his head, foul with corruption, serpents lap, his shaggy man bristles with vipers, and in his twisted tail a long snake hisses.
Seneca - Hercules Furens
Scylla has a similar mutability - sometimes having many heads, sometimes human down to the privates (Virgil - Aeneid) and having snake bits or wolverine/dog parts (or both!) below.
Anyway, back to the question:
While there is no explicit reference for or against, I believe that it is reasonable to assume that multi-headed creatures in Greek mythology had only one mind.
Aside from there being no understanding of the seat of consciousness being in the brain, as you point out, i'd add the following:
The monsters are always referred to in the singular. There are too many references to list, but in every translation I've seen it's always referred to as a single being unless talking explicitly about the heads (or other multiple appendage)
The appendages always seem to act in concert, with one purpose. Virgil gives us a good example of this, both from the Aeneid
The Sibyl, seeing the snakes bristling upon his neck now, threw him for bait a cake for honey and wheat infused with sedative drugs. The creature, crazy with hunger, opened its three mouths, gobbled the bait
Cerberus stood agape and his triple jaws forgot to bark.
- But the strongest point I think is referring to the Centimanes, one of whom speaks in Theogony:
And blameless Cottus answered him again: “  Divine one, you speak that which we know well: no, even of ourselves we know that your wisdom and understanding is exceeding, and that you became a defender of the deathless ones from chill doom. And through your devising we have come back again from the murky gloom and from our merciless bonds, enjoying what we looked not for, O lord, son of Cronos. And so now with fixed purpose and deliberate counsel we will aid your power in dreadful strife and will fight against the Titans in hard battle.” So he said: and the gods, givers of good things, applauded when they heard his word
Its worth noting here that by talking in the multiple ('we','our') I believe he is referring to himself and his brothers, also with him, not solely about himself, but because he speaks with one voice and one purpose implies one mind.
Have you ever tried to get 50 people to agree on anything?