So do we see the aliens at all?

Yes.

Although mostly confined to parts glimpsed here and there, via being casted in shadow or put only partially oncamera, we do more or less see them in their entirity throughout the course of the first season. In fact, "The Raising of Lazarus" gives us the biggest glimpse of an alien in one episode/of one alien (maybe a little too much, in my opinion, as I preferred their form to remain a bit clouded in whole). They prefer their natural state because why carry around a diseased human body if you don't have to? They are seen being revived from their catatonic state in their natural form, sneaking around for new hosts, and many walking around naked in the caverns of their headquaters - except the Advocacy and specially annointed underlingers who don contamination suits so as to bear the heat of the radiation levels because they're too important to suffer the side effects, but even then we see their bare hands poke out, as well as even glimpses at the back of their masked heads. In Season 2, they are human. Yes, a few glaring exposures in a couple of episodes, but throughout the centre of the season they are in total human form (never explaining the nature of their "human" bodies).

If you've seen the 1953 film, note that they bare resemblance, but are vastly re-designed to give them a bigger bulk, almost bear-like in size.

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Formless, faithless, and free.