Thomas says no (ST III.4.1). Human nature alone was fit for assumption by the Son, because humanity alone had the two characteristics that make such assumption fitting: first, the dignity of rational personhood which affords every human creature a congruence with the divine Word (thus excluding all creatures except for human beings and angels), and second, because of the necessity for “reparation,” “cum subiaceret originali peccato” (Ibid., corp.). Angels, while also sinful, are “unredeemable” (irremediable) (Ibid., ad 3).
Why is that? Earlier in ST, he quotes Damascene on this point: “Death is to men, what the fall is to the angels” (I.64.2.c., cf. De Fide Orth. ii). This is so, because “man’s will adheres to a thing movably, and with the power of forsaking it and of clinging to the opposite; whereas the angel’s will adheres fixedly and immovably. Therefore, if his will be considered before its adhesion, it can freely adhere either to this or to its opposite (namely, in such things as he does not will naturally); but after he has once adhered, he clings immovably” (Ibid.). Angelic knowledge and willing, Thomas thinks, is not discursive and piecemeal, as ours is, but rather simple: “in the truths which they know naturally, they at once behold all things whatsoever that can be known in them” (I.58.3).
If Thomas were wrong about the fixity of the angelic will, then there wouldn’t be any great reason that I can see to deny the possibility of the LORD’s assuming an angelic nature. I’m not certain that he is wrong about that, of course, but I have rather less confidence than he seems to in the conviction that this kind of speculative thought should command.