Yes. The intellect can understand its own act because the first thing understood of the intellect is its own act of understanding.
Intellectus potest suum actum intelligere quia primum quod de intellectu intelligitur, scilicet ipsum eius intelligere.
The object of the intellect is something universal, namely, "being" and "the true," in which the act also of understanding is comprised.
Obiectum intellectus est commune quoddam, scilicet ens et verum, sub quo comprehenditur etiam ipse actus intelligendi. Unde intellectus potest suum actum intelligere.
But not primarily, since the first object of our intellect, in this state of life, is not every being and everything true, but "being" and "true," as considered in material things, as we have said above (Q84, A7), from which it acquires knowledge of all other things.
Sed non primo, quia nec primum obiectum intellectus nostri, secundum praesentem statum, est quodlibet ens et verum, sed ens et verum consideratum in rebus materialibus, ut dictum est, ex quibus in cognitionem omnium aliorum devenit.
The human intellect neither is its own act of understanding, nor is its own essence the first object of its act of understanding, for this object is the nature of a material thing. And therefore that which is first known by the human intellect is an object of this kind, and that which is known secondarily is the act by which that object is known; and through the act the intellect itself is known, the perfection of which is this act of understanding. For this reason did the Philosopher assert that objects are known before acts, and acts before powers (De Anima ii, 4).
Intellectus humanus nec est suum intelligere, nec sui intelligere est obiectum primum ipsa eius essentia, sed aliquid extrinsecum, scilicet natura materialis rei. Et ideo id quod primo cognoscitur ab intellectu humano, est huiusmodi obiectum; et secundario cognoscitur ipse actus quo cognoscitur obiectum; et per actum cognoscitur ipse intellectus, cuius est perfectio ipsum intelligere. Et ideo philosophus dicit quod obiecta praecognoscuntur actibus, et actus potentiis.
Augustine says (De Trin. x, 11), "I understand that I understand."
Augustinus dicit, X de Trin., "intelligo me intelligere."