No. The soul does not know corporeal things through itself because the soul itself cannot be known through the bodily senses.
Anima non cognoscit corporea per suam substantiam quia ipsa anima non est cognoscibilis per corporis sensus.
If there be an intellect which knows all things by its essence, then its essence must needs have all things in itself immaterially; thus the early philosophers held that the essence of the soul, that it may know all things, must be actually composed of the principles of all material things. Now this is proper to God, that His Essence comprise all things immaterially as effects pre-exist virtually in their cause. God alone, therefore, understands all things through His Essence; but neither the human soul nor the angels can do so.
Si aliquis intellectus est qui per essentiam suam cognoscit omnia, oportet quod essentia eius habeat in se immaterialiter omnia; sicut antiqui posuerunt essentiam animae actu componi ex principiis omnium materialium, ut cognosceret omnia. Hoc autem est proprium Dei, ut sua essentia sit immaterialiter comprehensiva omnium, prout effectus virtute praeexistunt in causa. Solus igitur Deus per essentiam suam omnia intelligit; non autem anima humana, neque etiam Angelus.
Material things known must needs exist in the knower, not materially, but immaterially. The reason of this is, because the act of knowledge extends to things outside the knower: for we know things even that are external to us. Now by matter the form of a thing is determined to some one thing. Wherefore it is clear that knowledge is in inverse ratio of materiality. And consequently things that are not receptive of forms save materially, have no power of knowledge whatever: such as plants, as the Philosopher says (De Anima ii, 12).
Oportet materialia cognita in cognoscente existere non materialiter, sed magis immaterialiter. Et huius ratio est, quia actus cognitionis se extendit ad ea quae sunt extra cognoscentem: cognoscimus enim etiam ea quae extra nos sunt. Per materiam autem determinatur forma rei ad aliquid unum. Unde manifestum est quod ratio cognitionis ex opposito se habet ad rationem materialitatis. Et ideo quae non recipiunt formas nisi materialiter, nullo modo sunt cognoscitiva: sicut plantae, ut dicitur in II libro de anima.
But the more immaterially a thing receives the form of the thing known, the more perfect is its knowledge. Therefore the intellect which abstracts the species not only from matter, but also from the individuating conditions of matter, has more perfect knowledge than the senses, which receive the form of the thing known, without matter indeed, but subject to material conditions.
Quanto autem aliquid immaterialius habet formam rei cognitae, tanto perfectius cognoscit. Unde et intellectus, qui abstrahit speciem non solum a materia, sed etiam a materialibus conditionibus individuantibus, perfectius cognoscit quam sensus, qui accipit formam rei cognitae sine materia quidem, sed cum materialibus conditionibus.
Aristotle did not hold that the soul is actually composed of all things, as did the earlier philosophers; he said that the soul is all things, "after a fashion," inasmuch as it is in potentiality to all: through the senses, to all things sensible; through the intellect, to all things intelligible.
Aristoteles non posuit animam esse actu compositam ex omnibus, sicut antiqui naturales; sed dixit "quodammodo" animam esse omnia, inquantum est in potentia ad omnia: per sensum quidem ad sensibilia; per intellectum vero ad intelligibilia.
Augustine says (De Trin. ix, 3) that "the mind gathers knowledge of corporeal things through the bodily senses."
Augustinus dicit, IX de Trin., quod "mens corporearum rerum notitias per sensus corporis colligit".