There's definitely a similarity in style which is cool but I don't think it's from the Prometheus.
I'm finding it difficult to find proof that it is from the Prometheus, other than the fact that it says P-01 on it. I just find it difficult to imagine how a chunk of the Prometheus would manage to escape lv223's gravity when the ship exploded so close to the surface. But then again, this is the sequel to Prometheus.
I think it more likely that it's simply part of the ship that this new crew of explorers used to get to "uncharted paradise", but is in fact a planet inhabited by loads of davids.
Also, it just occurred to me, does anyone else think the deacon could've stowed away on the engineer ship shaw took? I mean, it never really shows for certain whether or not shaw had taken off before the deacon hatched. Only that it showed shaw taking off in a separate scene just before the scene with the deacon. So, there is actually a bit of an ambiguity here. PLUS, Ridley said there was gonna be every type of xeno in Alien: Covenant and what are the odds of there being 2 deacons created? Not high I imagine.