Strange though it might seem, Aquinas says “No” (ST III.4.3.c.). The Son assumes our human nature, and that nature is united with the divine in the very person of the Son, which means that the man Jesus isn’t assumed by the Son (that’s adoptionism), he is the Son. A human being, Aquinas cautions, “significat humanam naturam prout est nata in supposito esse” (Ibid.); but there is only one subject (suppositum, hypostasis) in Jesus, namely the person of God the Son. Talk about the economic Trinity being the immanent!
This article offers a nice instance of Aquinas’s approach to disagreeing with Augustine. In an objection, he quotes the good bishop as writing (pre-Ephesus, of course), “filius Dei hominem assumpsit” (ST III.4.3.1). Aquinas deals with this by counseling a generous hermeneutic: “huiusmodi locutiones non sunt extendendae, tanquam propriae, sed pie sunt exponendae, ubicumque a sacris doctoribus ponuntur” (Ibid., ad 1).