Yes. God has ideas of all things known by Him because ideas are principles of the knowledge of things and of their generation.
So far as the idea is the principle of the making of things, it may be called an "exemplar", and belongs to practical knowledge.
But so far as it is a principle of knowledge, it is properly called a "type", and may belong to speculative knowledge also.
Evil is known by God not through its own type, but through the type of good. Evil, therefore, has no idea in God, neither in so far as an idea is an "exemplar" nor as a "type".
God has no practical knowledge, except virtually, of things which neither are, nor will be, nor have been. Hence, with respect to these there is no idea in God insofar as idea signifies an "exemplar" but only insofar as it denotes a "type".
Genus can have no idea apart from the idea of species, in so far as idea denotes an "exemplar"; for genus cannot exist except in some species. The same is the case with those accidents that inseparably accompany their subject; for these come into being along with their subject. But accidents which supervene to the subject, have their special idea.
Divine providence extends not merely to species, but to individuals as will be shown later (Q22, A3).
Plato is said by some to have considered matter as not created; and therefore he postulated not an idea of matter but a concause with matter. Since, however, we hold matter to be created by God, though not apart from form, matter has its idea in God (but not apart from the idea of the composite: for matter in itself can neither exist, nor be known).