No. The dominations are not sent to minister because to be sent to external ministry properly belongs to an angel according as he acts by Divine command in respect of any corporeal creature, which is part of the execution of the Divine ministry.
Dominationes in ministerium non mittuntur quia mitti ad exterius ministerium proprie convenit Angelo, secundum quod ex divino imperio operatur circa aliquam creaturam corporalem, quod quidem pertinet ad executionem divini ministerii.
Now the angelic properties are manifested by their names, as Dionysius says (Coel. Hier. vii); and therefore the angels of those orders are sent to external ministry whose names signify some kind of administration. But the name "dominations" does not signify any such administration, but only disposition and command in administering.
Proprietates autem Angelorum ex eorum nominibus manifestantur, ut Dionysius dicit VII cap. Cael. Hier. Et ideo Angeli illorum ordinum ad exterius ministerium mittuntur, ex quorum nominibus aliqua executio datur intelligi. In nomine autem dominationum non importatur aliqua executio, sed sola dispositio et imperium de exequendis.
On the other hand, the names of the inferior orders imply administration, for the "Angels" and "Archangels" are so called from "announcing"; the "Virtues" and "Powers" are so called in respect of some act; and it is right that the "Prince," according to what Gregory says (Hom. xxxiv in Evang.), "be first among the workers." Hence it belongs to these five orders to be sent to external ministry, not to the four superior orders.
Sed in nominibus inferiorum ordinum intelligitur aliqua executio, nam "Angeli" et "Archangeli" denominantur a denuntiando; "virtutes" et "potestates" dicuntur per respectum ad aliquem actum; "principis" etiam est, ut Gregorius dicit, inter alios operantes priorem existere. Unde ad hos quinque ordines pertinet in exterius ministerium mitti, non autem ad quatuor superiores.
The Dominations are reckoned among the ministering angels, not as exercising but as disposing and commanding what is to be done by others; thus an architect does not put his hands to the production of his art, but only disposes and orders what others are to do.
Dominationes computantur quidem inter Angelos ministrantes, non sicut exequentes ministerium, sed sicut disponentes et mandantes quid per alios fieri debeat. Sicut architectores in artificiis nihil manu operantur, sed solum disponunt et praecipiunt quid alii debeant operari.
Two accounts may be given in assigning the number of the assisting and ministering angels. For Gregory says that those who minister are more numerous than those who assist; because he takes the words (Daniel 7:10) "thousands of thousands ministered to Him," not in a multiple but in a partitive sense, to mean "thousands out of thousands"; thus the number of those who minister is indefinite, and signifies excess; while the number of assistants is finite as in the words added, "and ten thousand times a hundred thousand assisted Him."
De numero assistentium et ministrantium duplex ratio haberi potest. Gregorius enim dicit plures esse ministrantes quam assistentes. Intelligit enim quod dicitur, millia millium ministrabant ei, non esse dictum multiplicative, sed partitive; ac si diceretur, millia de numero millium. Et sic ministrantium numerus ponitur indefinitus, ad significandum excessum; assistentium vero finitus, cum subditur, et decies millies centena millia assistebant ei.
This explanation rests on the account of the Platonists, who said that the nearer things are to the one first principle, the smaller they are in number; as the nearer a number is to unity, the lesser it is than multitude. This opinion is verified as regards the number of orders, as six administer and three assist.
Et hoc procedit secundum rationem Platonicorum, qui dicebant quod quanto aliqua sunt uni primo principio propinquiora, tanto sunt minoris multitudinis, sicut quanto numerus est propinquior unitati, tanto est multitudine minor. Et haec opinio salvatur quantum ad numerum ordinum, dum sex ministrant, et tres assistunt.
Dionysius, however, (Coel. Hier. xiv) declares that the multitude of angels surpasses all the multitude of material things; so that, as the superior bodies exceed the inferior in magnitude to an immeasurable degree, so the superior incorporeal natures surpass all corporeal natures in multitude; because whatever is better is more intended and more multiplied by God. Hence, as the assistants are superior to the ministers there will be more assistants than ministers.
Sed Dionysius ponit, XIV cap. Cael. Hier., quod multitudo Angelorum transcendit omnem materialem multitudinem; ut scilicet, sicut corpora superiora transcendunt corpora inferiora magnitudine quasi in immensum, ita superiores naturae incorporeae transcendunt multitudine omnes naturas corporeas; quia quod est melius, est magis a Deo intentum et multiplicatum. Et secundum hoc, cum assistentes sint superiores ministrantibus, plures erunt assistentes quam ministrantes.
In this way, the words "thousands of thousands" are taken by way of multiplication, to signify "a thousand times a thousand." And because ten times a hundred is a thousand, if it were said "ten times a hundred thousand" it would mean that there are as many assistants as ministers: but since it is written "ten thousand times a hundred thousand," we are given to understand that the assistants are much more numerous than the ministers.
Unde secundum hoc, millia millium legitur multiplicativae, ac si diceretur, millies millia. Et quia decies centum sunt mille, si diceretur, decies centena millia, daretur intelligi quod tot essent assistentes, quot ministrantes, sed quia dicitur, decies millies centena millia, multo plures dicuntur esse assistentes quam ministrantes.
Nor is this said to signify that this is the precise number of angels, but rather that it is much greater, in that it exceeds all material multitude. This is signified by the multiplication together of all the greatest numbers, namely ten, a hundred, and a thousand, as Dionysius remarks in the same passage.
Nec tamen hoc pro tanto dicitur, quia tantus solum sit Angelorum numerus, sed multo maior, quia omnem materialem multitudinem excedit. Quod significatur per multiplicationem maximorum numerorum supra seipsos, scilicet denarii, centenarii et millenarii; ut Dionysius ibidem dicit.