(N/A) Yes,the convex lens will form a complete image of an object,even if its one-half is covered with black paper. This can be understood by the following two cases:
Case $I$: When the upper half of the lens is covered.
In this case,rays of light coming from the object will be refracted by the lower half of the lens. These rays meet at the other side of the lens to form the image of the given object.
Case $II$: When the lower half of the lens is covered.
In this case,rays of light coming from the object are refracted by the upper half of the lens. These rays meet at the other side of the lens to form the image of the given object.
Note: Although the image is complete,its intensity (brightness) will be reduced because fewer light rays are passing through the lens to form the image.