No, there is nothing all that specific about vector spaces. This is true about general algebraic structures.

What you want to care about here is preserving structures: How would you define addition on a disjoint union? e.g. If you have V⊔W you can add two things in V and you can add two things in W, but what about something in V with something in W? Which zero vector is "the" zero vector?

If you don't have all those properties that make a vector space, then it's just a set. Then, yes, if for some reason you want to do the sum of vector spaces V and W as sets, you will get the disjoint union of these sets. That would be a pretty odd thing to do though; in that case, why are they vector spaces?