No. The intellect knows itself not by its essence, but by its act, because it understands itself according as it is made actual by the species abstracted from sensible things, through the light of the active intellect, which not only actuates the intelligible things themselves, but also, by their instrumentality, actuates the passive intellect.
Non per essentiam suam, sed per actum suum se cognoscit intellectus noster quia seipsum intelligat intellectus noster, secundum quod fit actu per species a sensibilibus abstractas per lumen intellectus agentis, quod est actus ipsorum intelligibilium, et eis mediantibus intellectus possibilis.
An angel apprehends his own essence through itself: not so the human mind, which is either altogether in potentiality to intelligible things (as is the passive intellect) or is the act of intelligible things abstracted from the phantasms (as is the active intellect).
Angelus suam essentiam per seipsum apprehendit. Non autem intellectus humanus, qui vel est omnino in potentia respectu intelligibilium (sicut intellectus possibilis) vel est actus intelligibilium quae abstrahuntur a phantasmatibus (sicut intellectus agens).
It is said (De Anima iii, 4) that "the intellect understands itself in the same way as it understands other things." But it understands other things, not by their essence, but by their similitudes. Therefore it does not understand itself by its own essence.
Dicitur in III de anima, quod "intellectus intelligit seipsum sicut et alia". Sed alia non intelligit per essentias eorum, sed per eorum similitudines. Ergo neque se intelligit per essentiam suam.