Splashing yourself with a potion that has Saturation edited onto it through the CustomPotionEffects list tag renders you with no Saturation effect.
You can use the following command to generate such a potion to test with:
/give @p minecraft:splash_potion 1 0 {CustomPotionEffects:[{Id:23,Amplifier:0,Duration:1}],Potion:"minecraft:empty"}
More info: https://bugs.mojang.com/browse/MC-25866?focusedCommentId=317943&page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel#comment-317943
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And how would you go about getting a "Splash Potion of Saturation"? There's no such thing listed on the potions page on the wiki.
@Torabi - It's accessed through the /give command, with potion effect 23 as the CustomPotion modifier.
I would very much like to see this bug patched, I had hoped to include Splash potions of Saturation in an important gameplay mechanic of a Custom Map I had been working on, but was unpleasantly surprised to find this bug in the process.
Fingers crossed Mojang gets to this in the near future! (:

This is likely Working as Intended for the time being, as a potion with the saturation effect cannot be acquired through normal gameplay mechanics. There are many aspects to potion brewing that were left incomplete, but hopefully Mojang will revisit potions in the future.

Invalid as it refers to unimplemented things
I think that you misunderstand.
I can drink a potion that has saturation as a custom potion effect, and receive the saturation effect. However, I can not splash a splash potion that has saturation as a custom potion effect, and receive the saturation effect.
The fact that this is not implemented is the bug, as this is not the case with literally every other potion effect, such as Health Boost (Id:21) which is an effect that cannot be obtained through, as Torabi said "...normal gameplay mechanics."
I think that this should be reopened, unless the fact that I can splash myself with health boost is a bug.

This is comparable with the Giant: A feature that is actually in the game, but can only be used by special means, not actually supported by the developers.
How is this comparable with the giant?
Because, to me:
Potions are something that are available to all players of the game on the front end. Giants can only be accessed through either commands or NBT editing. The fact that one thing is broken with one potion does not mean that it is an idea that fell by the wayside of the developer, it just means that it's broken, and is a bug.
How is this just something that isn't supported by the developer?

The saturation potion is, to my knowledge, only implemented for technical reasons, to make things work behind the scenes.
However, since I don't have 100% developer confirmation and I don't really want to poke one now: Reopened.

Confirmed for
15w44b as the normal drinkable potion works I would see this as a valid bug

Confirmed for 1.10.2.
This is highly related to MC-98123, and most of the code analysis there applies here as well (the same usage of affectEntity
is found in EntityPotion
).

Confirmed for 17w50a.
Seems to be somehow related to MC-121429 and how Minecraft processes instant effects in potions.
Confirmed.