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The Materialization Manifestation is different from angelic Cover. The first is an effect activated by an angel by her choice to achieve some goal; the second is a state created and maintained by the GodMachine when it installs an angel on some mission.
The Discorporate Manifestation certainly applies in the first case, but can an angel in Cover choose to Discorporate? I ask because there are consequences for combat if an angel can escape whenever it wants.
The Manifestations are separate from an Angel's Cover and Discorporate is a valid Manifestation for an Angel with Cover.
Looking at the Example Angels in the Storytelling & Antagonists section of Demon the Descent (starting on p218) we have 5 Angels and all of these examples include the Discorporate Manifestation. While Cover isn't handled as a stat for an Angel like it is for a Demon, the Description and Methods sections of each write up make it clear that these are Angels with Cover. All of these Angels also have the Materialize Manifestation which might cause some confusion as to how these all interconnect. However, in The God Machine Chronicle rule book we have more examples of Angels in other permutations. Mr Nose (p138) has Materialize, but not Discorporate. Serotonin (p141) has Discorporate but not Materialize.
We can also find an inferred ability for an Angel in Cover to discorporate as a means of escape in the Demon: Interface collection of short fiction. In the story Time to Go, an Angel named Rook is using a Cover named Gill. In the scene where Rook is destroyed we get the line, "Rook’s eyes widened, but he had no time to flee or discorporate."
It is completely valid to make the argument that any supernatural effect, including completely discorporating in a crowded area, would put a strain on Cover (cause a Compromise). But the rules for that are written from a PC Demon perspective. They even explicitly state "A demon's Cover is cut off from the God-Machine's self-corrective Infrastructure, which means that when a demon strains her Cover it can grow out of sync with reality..." This implies that the self-corrective Infrastructure that is still attached for an Angel would keep the Cover intact despite supernatural actions by the Angel. This being a Storytelling game, it would be completely valid for a Storyteller to put limits on this Infrastructure for the purposes of telling an interesting story, but it's not explicitly in the rules that the Cover would break in response to Discorporate.
That said, it's not the case that choosing to Discorporate is completely without cost. The Angel loses all Corpus in the process the same as if it had taken lethal damage of that amount. For some definitions, that would count as "killing" the Angel. The Combat section for Ephemeral Beings: Ghosts, Spirits, and Angels (p343) explains that the being goes into hibernation and is out of commission: "As the entity can't act while hibernating, this means waiting for the one Essence a day for being in a suitable area to slowly build up to Corpus, and that more powerful entities take longer to recover from being 'killed.'"
Thematically, just surviving a combat encounter with an Angel should be considered a win. Demon the Descent describes itself as a game of Techgnostic Espionage. Generally one is looking to hide from Angels and simply survive the encounters they can't hide from rather than aiming to put them down permanently.
However, if you are looking for a permanent solution to a particular Angel, then what you need is to discover the Angel's Bane (p342). A Bane can affect an Angel even when in Twilight and the examples given explicitly mention killing Angels permanently: "A mid rank angel can be killed by a weapon dusted with the ground-up remains of a meteorite" or "A high Rank angel can't willingly touch the sigils of a certain incantation in Sumerian and dies if the signs are carved into the flesh of its host." You will see example Banes on all of the sample Angels mentioned earlier and any Demon player should be able to work with the Storyteller to investigate and discover both the Bane of an Angel as well as the place it reforms (probably Infrastructure). So, if it tries to Discorporate to escape a combat, that's fine. Now you know where to find it and it will be helpless there against its Bane.
