No, they are not immune, but resistant.
From the Demon:The descent (Page 198) describing demonic forms:
Sense the Angelic
All angels are agents of the God-Machine and are capable
of recognizing that connection when they encounter each
other. The Cover that demons adopt shields them from angelic
scrutiny. Some angels are designated to seek and destroy nonangelic
supernatural entities, such as demons. Demons who
retain this ability have adapted it to work in reverse, making it
easier for them to sense angelic beings.
From this fragment you can see that even without having this form they are sometimes able to discover angels, but without having this supernatural sense it might be very difficult. So having this ability demon would easily find that your cousin, living in the basement since high school is in fact angel that appeared yesterday, without it they will have much harder work. Still, even with this power its far cry from being completely immune:
The demon can sense the use of angelic powers
on people and places. Anytime the demon is in an area where
an angel has used Numina in the past 24 hours, or if she
encounters a person that is currently under the effects of an
angel’s Numen, roll Wits + Investigation to notice the effect.
If she has encountered the power before, she can positively
identify exactly which Numina was used.
Oh, obviously to use that you have to assume demonic form... so doing in front of your "older bother" you will blow your cover.
After reading a bit more I have found this fragment:
Those [demons] who survive learn to keep a constant, vigilant watch
for signs that angels have found them. They have one great
advantage over their new human neighbors in keeping out of
the way — they’re still angelic enough that none of the mind
tricks, illusions and spatial folding the God-Machine uses to
conceal its facilities work on them.
Demons always see the gears, always perceive facilities and
can sense when Infrastructure has been built or an occult
matrix is forming [..] Braver demons hijack Infrastructure, stealing new
Cover identities before angels have time to manifest into them
So I have to change my answer a bit:
No, they can't simply recognise angel by looking at someone, it requires quite an effort.
They can sense that something is happening nearby and that reality has been changed.
So, if you'd go on a camp trip and meanwhile angel used your existing brother as a cover - you wouldn't easily find that, but if you never had brother before and suddenly there is one sitting at the table - well, you will know that the reality has been warped. You would probably have implanted memories of you two growing together but you'd know that they are false.
Still, if the cover and infrastructure was very subtle - "Your brother was living until now with your stepmother that you hate and never visit and now decided to drop in" - demon could fell for it.