No because fungi are bottom feeders of the ground and yet mushrooms are kosher.
The issue is whether or not these are creatures according to Torah. From Leviticus 11:
These you may eat of all that live in water: anything in water, whether in the seas or in the streams, that has fins and scales—these you may eat.
But anything in the seas or in the streams that has no fins and scales, among all the swarming things of the water and among all the other living creatures that are in the water—they are an abomination for you
and an abomination for you they shall remain: you shall not eat of their flesh and you shall abominate their carcasses.
Everything in water that has no fins and scales shall be an abomination for you.
Now, I am going to reference Bible hub here mostly because they have a nice Strong's Hebrew concordance feature that sefaria doesn't have that is easy to copy and paste from.
But basically I would argue that the important words we have to distinguish here are:
Noun - masculine singular construct
Strong's 8318: A swarm, active mass of minute animals
Article | Adjective - feminine singular
Strong's 2416: Alive, raw, fresh, strong, life
Strong's 5315: A soul, living being, life, self, person, desire, passion, appetite, emotion
So. Is coral an active (teeming) mass of minute animals? Well. It is a living colony in the same way that mushrooms are colonies of living things. But other things that swarm or teem are like... krill. shrimp. Locusts. Flies. Ants.
Y'know, stuff that moves. Swarms. Coral doesn't teem or swarm. It's static.
Which leaves us with living and creatures.
I would argue again that "living" implies regular movement — for example, you can have living waters. (Same root word for mayyim chayyim).
But also the other terms which appear beside the root word for life/living over and over again are basically:
Creeping, moving (Strong's 7430 רָמַשׂ ramas)
Flesh (Strong's 1320 בָּשָׂר basar)
Flying or soaring (5774 עוּף)
Having a soul (or literal breath) (5315, נֶפֶשׁ)
And nefesh is of course, also the last one in that list!
So is coral alive in the way Torah usually means things are living beings? Well, coral doesn't creep or move. It also doesn't have blood (which, arguably, means it can't have a carcass. It sort of has bones! But no carcass). It...MIGHT have flesh? I'm sort of unclear about this.
Do corals have flesh? and,
do corals have souls? And if not metaphorically souls, do they have breath?
Well, coral do respirate. But so do plants. And neither of them have lungs. Also according to @montereybayaquarium's website coral get oxygen from algae? (Don't worry Monterey bay aquarium no one is actually going to eat the coral, this is all hypothetical)
Coral reefs get their bright colors from the algae — called zooxanthellae — living in their tissues. The zooanthellae provide the coral polyps with oxygen and nutrients produced from photosynthesis. In return, the coral polyps provide zooanthellae with carbon dioxide (a byproduct of the polyps’ “breathing” oxygen) and shelter.
Coral polyps can have mouths, but they don't really breathe with lungs. So I'm not sure they have that kind of nefesh (breath of life). And corals are like, a bunch of skeletal base material with living polyps on the top. But are they fleshy? But all their color comes from the algae living in them.
For this I go back to the presence of blood being a big factor, because again, mushrooms have flesh but don't have blood, and so halakhically...that fungi is a plant.
Also apparently Octocorals don't have those exoskeletons? So at that point how would we know something is an octocoral versus like...a seaweed?
I think either seaweed isn't meant to be kosher, or actually corals are kosher because seaweed is. Oysters have gills and hearts. Scallops have a gajillion eyes. Really easy to see those aren't plants.
Basically if you look at a coral does it have a breath and soul, does it fly or creep, does it bleed, does it have flesh, does it move around in general? Could it possibly be a plant, halakhically speaking? (Not by scientific taxonomy!) Would bronze age folks look at it and go "yeah, that's a plant."? Also important: what IS a plant? Halakhically?
Many such questions. Anyways I don't think corals have souls.