The Exploit's rules are sparse, but ephemeral beings have their own analogous Manifestation Effect, Possess, and while they're possessing a host, they lose all access to their supernatural powers (Influences and Numina).
Angels, as ephemeral beings, possess people under those same limitations. And 'under the hood,' so to speak, those angelic Numina (that they lose access to) use the exact same metaphysical subroutines that, after the Fall, demons (re-)learn to utilize more consciously, in the form of Embeds and Exploits.
As angels, all servants of the God-
Machine are aware of these pathways, but they make use of
them differently. Angels do not make conscious effort to use
Embeds, they are able to do so simply as part of their missions.
Given that, it's a safe assumption that angelic possession is made possible by the same metaphysical laws that demonic possession is, which implies the limitations (no ability to access any of the God-Machine's subroutines while in a host) are shared.
Also, access to Embeds and Exploits is not just a matter of mere demonic cunning or even conscious, detailed knowledge of metaphysics and the God-Machine's backdoors in reality. A demon couldn't teach a human to use them no matter how much they tried to learn, and there are other instances where demons are known to lose access to them temporarily, despite continuing to retain their theoretical knowledge of them. Like when a demon becomes temporarily fully human with the Going Native Embed (Flowers of Hell p102).
Losing access to them when one's demonic form has transubstantiated into an 'insubstantial energy' form, as happens to perform Possession, would also plausibly lose access to Embeds and Exploits, as any relevant 'machinery' is not in its usual shape. This also makes the Dramatic Failure case of the Possession Exploit actually dramatic, as it means, while stuck in energy form, the demon is truly helpless and incapable of any Embeds or Exploits aside from re-attempting Possession.