I don't find anything that specifically forbids this. However, you would think the Angel would be able to detect the demon if he fails a compromise roll.
Reading the description for Deep Cover Embed from Flowers of Hell:
Like demons and angels, many supernatural beings hide behind a mask of mortality. They’re just not as good at it. This Embed operates under the principle that such creatures have two identities — one with a detectable occult connection and one without — and temporarily applies that duality to the demon’s Cover.
So its principle works for beings that have the false appearance of being human. That includes ephemeral beings that have the Mortal Mask Numen, which some spirits and angels do. (Though in the context of Demon, this is also called the angel's Cover.)
Whenever the demon would have the option of using Spoof (p. 112 of Demon), she may instead use this Embed. Rather than appearing as an ordinary human when targeted by an effect meant to reveal her nature, the demon appears to be a supernatural being.
Spoofing being the reflexive ability to appear as an ordinary human being to supernatural detection attempts.
A demon cannot spoof in demonic form, for obvious reasons.
So yes, Deep Cover is definitely generic enough to allow appearing to be another angel concealing itself as a human using the Mortal Mask Numen. It could also appear to a spirit as another spirit that's using the same Numen. (Short of an Exceptional Success, there are only two choices for what to appear as: "the same type of supernatural being" or a new type they have never seen before, so appearing as an angel/spirit usually only works on an angel/spirit)
That said, consider what the investigating angel will think when it attempts to discern the target's nature and it gets a result saying that it's another angel. In most cases this would actually raise more questions in its mind than it answers, compared to if the demon had simply spoofed as a mere boring, irrelevant human. It seems more likely to dig yourself into a deeper hole, if the angel has any reaction that isn't ignoring this 'other' angel as irrelevant to its own mission.
And even if it's the suspicious type, while it could follow up with attempt to upload a request to check the God-Machine's Rolodex for if the target is in the employee directory, even that wouldn't be evidence that its senses had been fooled, because some angels become disconnected from the God-Machine without Falling into demonhood: exiles.
Some exiles can still both hear and respond to the voice of the God-Machine. Others find they can hear their creator but cannot speak to it, or at the very least it does not choose to respond in turn. Most lose all contact with the God-Machine when they become exiles and so often describe themselves as the Abandoned. They did not Fall and cannot choose to do so. Angels usually avoid exiles or ignore them. The God-Machine almost never sends hunter angels to reclaim exiles, so some have spent decades or even centuries on Earth.
All that said... while you theoretically can spoof an angel or spirit, in practical terms, this situation will never actually occur, because as written, no angel or spirit would have the (possibly far too useful) capability to identify specific types of supernatural beings. Angels and spirits use Numina, and none of the Numina in the Demon: the Descent book can identify what class of supernatural being a target is. The opportunity to spoof them, whether appearing as human or using Deep Cover, can't occur without an actual ability like that. An ST would have to invent one, and angels at least are a potent threat already without such an ability. As it is, they can delegate to loyal stigmatics with potentially demon-detecting abilities like Aura Reading.
There is no such rule saying you cannot spoof an angel. Angels are not omniscient. Not even the god machine is omniscient however if you are compromised in front of an angel then you will receive burnt status which will make spoofing the angel impossible until you find a new cover.