It dependes what kind of smoothing.
I don't know about new versions of Blender, so I don't know the functionality you are talking about, but it sounds like it is keeping the mesh the same but using it as a base mesh for a high resolution smooth surface. The number of vertices are the same, but a high res smooth surface is constructed at as a preprocessing stage while rendering.
However, (although I don't think you are talking about this) setting smoothing on a mesh's material can mean fewer vertices, since shared vertices can be reused (if the position, normal and uv coordinates are the same).
So to summarise:
Any kind of subdivision smoothing -> more vertices
Setting material smoothing flag -> fewer vertices
However, if you are using subdivision, when you export it may just export the base mesh. You may need to apply the subdivision modifier to be able to export the smooth geometry.
Why don't you just look at the number of vertices and number of triangle when you export?