There's no such thing as a MTB chain though Shimano does I believe sell them as such. Any 9 speed chain will work. And yes, you could put a MTB derailler and cassette on your road bike and it would work just fine. With your double crank, you could get away with a medium cage MTB rear derailler, though the long cage would only be a tiny weight penalty and give you the option of going to a triple if you decided to eventually. The biggest downside to using a MTB cassette in place of a triple crankset is the jumps between gears. It's a personal thing. I didn't mind at first but switching back to a road cassette for a while made me want a road cassette all the time.