Not exactly. A unicellular organism is a living thing made up of one cell. But cancer cells are not invaders from outside the body. Think of cancer cells as traitors within us--cells that stabbed us in the back.
Here's what happens. Our cells die all the time, but they also reproduce by splitting in half (this is called cellular fission). Sometimes tho, the programming of a cell gets screwed up. That cell doesn't know when to stop dividing and soon you have more and more and more cells with screwy programming. These cells are cancerous, and they are your own cells.
Ever see that Halloween episode of 'The Simpsons' when Homer's hammock makes copies of him and the military worries that soon there will be so many of them that they blot out all other life? That's the same thing basically--cancer.
So, in short....cancer cells are part of the living thing that has cancer, so they are not separate organisms (unicellular or otherwise).