It is indeed possible to grow bamboo outdoor in NW Connecticut, or any other part of Connecticut for that matter. However, I would caution you against this because bamboo, especially running bamboo, can have adverse effects on the environment. If not watched, they can overrun crop fields. Check out the details on www.bamboogarden.com/care.htm.
You might be able to grow certain varieties in protected areas; but if and when they do take hold and begin spreading they are extremely difficult to keep under control! They are indeed a very invasive plant and not great for environments that are not native. If it's the look of Bamboo you are after; there are some of the less invasive Clumping Grass species which would grow up in the North East and give a similar effect.
Eh... not really. It may be grow okay during the summer, but I don't think bamboo could survive CT's winters. You can try growing some bamboo in large pots outdoors, just be sure to bring them indoors around the end of September, or before the outside temperature goes below 60 degrees. :)