No, an "alphaed out area" is not the same as deleting those polygons.
In any raytracer (such as Cycles or Evee), a ray is cast (either from the light source into the camera or from the camera to the light source, I do believe, but somebody else can tell me if it's wrong, that in Blender we do the latter).
If this ray now has to go through one of these holes:
a.) If its cut out, it just goes through
b.) If its alpha, the ray hits the mesh, looks up the material, looks up the uv unwrapping, then decides that it has nothing to show and travels on with its path.
This said, adding a lot of more polygons to accomodate for the holes, will affect your blender file's size and the RAM usage.
There is no better or worse, its "case sensitive". For making trees, e.g. , some tutorials suggest to not use alphas, but cut the leave's plane to the mapped leaf texture (because then you could have ray intersecting hundres of leaves, but only in its alpha regions and slowing it down unneccessary).