That's what we did in our house for the most part. Our livingroom/kitchen/up and downstairs hallway are a tan color, our bedroom is a chocolate milk color. Our bathrooms are funky colors though, lol.
Absolutely. Using multiple colors from the same paint sample strip is a pretty fail safe way of coordinating a house while maintaining a little contrast between rooms.
I don't see why not. It's a lot better, imo, than a palette of crazy colors everywhere.
My downstairs is all neutrals, with the kitchen and dining rooms darker versions of the family and living rooms (which are different colors but so close in the lighter shades that it's really a "why did we bother?") and the colors run through the hallways, stairwell and upstairs loft area and skylight. The bedrooms, bathrooms and office are whatever we decided to paint since you can't see them if the door is closed anyway.