Could cancer be in itself a evolutionary process?
Interesting question. I believe it definitely is an evolutionary process. unicellularity breaking away from a multicellular life. 

There are two examples that I can think of, which can support this argument:


Hela cells: Hela cells have been classified as a different organism because they have the ability to grow outside the host indefinitely and their genome is different from Homo sapiens. Hela cells also have a new scientific name- Helacyton gartleri
Transmissible tumors: two tumors have been known to infect other hosts and therefore can be called obligate pathogenic lifeforms. One is Devil Facial Tumor Disease which infects Tasmanian devils and gets transmitted by biting. Another is Canine Transmissible Venereal Tumor which infects dogs and spreads via sexual route. 



  Could it be possible that in rare cases it could lead to the development of new organs or specialized cells?


Cancer as of now has a pathogenic identity. It is a simplistic process which in a thermodynamic point of view can be described as maximization of entropy(disorder) and thereby increasing the stability [like the way solutes diffuse]. If a cancer has to give rise to a new functional organ then it has to be supportive of the ordered lifestyle which it is trying to break away from in the first place. It may adopt a pathogenic lifestyle initially and then may redevelop order. I don't know of any such evolutionary event but it may nonetheless be possible.