Most people seem to think so, including Aristotle. But look at the way in which Socrates first raises the issue in the Protagoras:
What’s interesting about this is that the relations between knowledge (or wisdom) and the feelings mentioned here (anger, pleasure, grief, love, fear) are understood as relations of power. The word translated here as be in command is standardly translated rule. Two things seem to follow from this. First, the view which Socrates is presenting here – which is surely presented as his own view – seems to depend on the possibility of conflict between different parts of the self. Secondly, in presenting one part as in command or ruling, this view effectively treats the self as a political entity.
That is, even at this point in the Protagoras, Socrates seems to be expressing exactly the kind of view of the self which finds its full development in the Republic. Since that view seems to depend on the possibility of disagreement between different factions, as it were, within the person, and the argument against akrasia in the Protagoras seems to depend on denying the possibility of the same person having contradictory beliefs at the same time, it’s hard to see how the Socrates who holds this view before the beginning of the Protagoras argument can really accept the Protagoras argument itself.
Have you seen this image of a well-known visual illusion, the Müller-Lyer lines?
The two horizontal lines are the same length, but look to be different lengths because of the chevrons added to them. When you look at them do you think that they are the same length and that they are not the same length at the same time? Well, that looks as if it’s exactly what Plato would have thought, at least at the time of writing Republic X. Here’s how he opens the discussion of this kind of thing in Republic X:
No, it doesn’t.
And the same things look bent in water and straight out of it, and things look both concave and convex because of the way colours mislead our sight, and we clearly have every other similar confusion present in our souls.
And here’s what he says about this kind of case:
Indeed they have.
And these are the work of the reasoning part of the soul.
But it often happens that when this part of the soul has measured things and indicated that some are bigger or smaller than others, or that some are equal to others, the opposite seems to be true of them at the same time.
And didn’t we say that it was impossible for the same thing to have opposing beliefs about the same thing at the same time?
And rightly, too.
So the part of the soul whose beliefs conflict with the results of measurement couldn’t be the same as the part whose beliefs match the results of measurement.
No, it couldn’t.
What we have here is Plato describing being consciously subject to sensory illusions. He seems to say that when we are consciously subject to sensory illusions, we have contradictory beliefs at the same time. That’s possible, because the contradictory beliefs are held by different parts of the soul
Since there is a conscious reference here to the discussion in Republic IV, it seems clear that at least by the time he wrote Republic X, Plato thought both these two things:
Putting these two points together it seems that at the time of the Protagoras, Plato already has the key commitments of the Republic’s view of the soul. And at the time of the Republic, he clearly does not hold the views of Ordinary Jo.