Does adding the Campaign's Dependencies lag the map a bit more? Or does it increases the map's loading time?
Basically, I'm wondering if adding Dependencies only to get one single little thing out of it is inefficient. If it is, I'd like to know how to extract only one thing out of it.

It does increase the map's loading time, although I am not sure by how much.

Okay, so are there any ways to extract only one particular item from a dependency?

I would guess: no.
But you could copy the units into your map. But it's not worth it.

The amount of time the campaign dependency adds to loading the map will be extremely negligible I would imagine.

Besides - I think... and again this is purely me thinking here, nothing concrete or factual of course... I think that when the map is compiled, as in loaded/tested or ran - it only loads the Data objects (effects, behaviors, units, abilities, buttons etc) which it requires. This might require someone with a lot more knowledge than myself to clarify. But I think a blank map with 4 dependencies and no triggers will have a very similar loading time to a map with only Multiplayer Mod dependency loaded...

As for causing lag? As in latency/multiplayer generated delay etc... a dependency shouldn't cause any of this.

yes, AFAIK I know from my beta mapping time on my laptop. the unit's models are loaded pretty late. At least my laptop had a noticeable lag after creating 10 sentries. But it wasn't that big with Marines or Zerglings.

Some effects are shown AFTER their first use. E.g. Firebat's attack's flames. Btw, only the first loading of everything in sc2 is slow. If that's your second game without closing sc2, it will load much much faster.