Yes. God has immediate providence over everything because He has in His intellect the types of everything, even the smallest, and whatsoever causes He assigns to certain effects, He gives them the power to produce those effects, whence it must be that He has beforehand the type of those effects in His mind.
Two things belong to providence--namely, the type of the order of things foreordained towards an end; and the execution of this order, which is called government.
There are certain intermediaries of God's providence for He governs things inferior by superior, not on account of any defect in His power, but by reason of the abundance of His goodness; so that the dignity of causality is imparted even to creatures.
Thus Plato's opinion, as narrated by Gregory of Nyssa (De Provid. viii, 3), is exploded. Plato taught a threefold providence. First, one which belongs to the supreme Deity, Who first and foremost has provision over spiritual things, and thus over the whole world as regards genus, species, and universal causes. The second providence, which is over the individuals of all that can be generated and corrupted, he attributed to the divinities who circulate in the heavens; that is, certain separate substances, which move corporeal things in a circular direction. The third providence, over human affairs, he assigned to demons, whom the Platonic philosophers placed between us and the gods, as Augustine tells us (De Civ. Dei, 1, 2: viii, 14).
Note RO3: It is better for us not to know low and vile things, because by them we are impeded in our knowledge of what is better and higher; for we cannot understand many things simultaneously; because the thought of evil sometimes perverts the will towards evil. This does not hold with God, Who sees everything simultaneously at one glance, and whose will cannot turn in the direction of evil.