Yes. To each man an angel is appointed to guard him, and such guardianship belongs to the lowest order of the angels (whose place it is, according to Gregory, to announce the "lesser things"), because it seems to be the least of the angelic offices to procure what concerns the salvation of only one man.
Singulis hominibus singuli Angeli ad custodiam deputantur, et talis custodia pertinet ad infimum ordinem Angelorum (quorum, secundum Gregorium, est minima nuntiare), quia hoc videtur esse minimum in officiis Angelorum, procurare ea quae ad unius hominis tantum salutem pertinent.
The other kind of guardianship is universal, multiplied according to the different orders. For the more universal an agent is, the higher it is.
Alia vero est custodia universalis. Et haec multiplicatur secundum diversos ordines, nam quanto agens fuerit universalius, tanto est superius.
Thus the guardianship of the human race belongs to the order of "Principalities," or perhaps to the "Archangels," whom we call the angel princes. Hence, Michael, whom we call an archangel, is also styled "one of the princes" (Daniel 10:13). Moreover all corporeal creatures are guarded by the "Virtues"; and likewise the demons by the "Powers," and the good spirits by the "Principalities," according to Gregory's opinion (Hom. xxxiv in Ev.).
Sic igitur custodia humanae multitudinis pertinet ad ordinem principatuum, vel forte ad Archangelos, qui dicuntur principes Angeli, unde et Michael, quem Archangelum dicimus, unus de principibus dicitur Dan. X. Ulterius autem super omnes naturas corporeas habent custodiam virtutes. Et ulterius etiam super Daemones habent custodiam potestates. Et ulterius etiam super bonos spiritus habent custodiam principatus, secundum Gregorium.