Hi,
It all depends on the scene and the added object. As mentioned by others, if the added object is reflected, you will need to find the region (or selection) of it, and do a region/selected render.
Rendering added object with shadows is actually quite tricky, because when doing render selected, only the geometry of the object is used as a mask, without its shadows and reflections, obviously. So, if it is a somewhat non-reflective object with somewhat static shadows, with somewhat stable camera, you can probably make it work using region rendering, and the overlaying on top of the original.