Will an 8" 100w bookshelf speaker work on stage or outdoors with good results?

Certainly not, the speakers have a place for,

It's like asking you if a small car can pull a rock like a tractor.

Outdoor to the door of the high-power speakers and amplifiers, if you do not pursue a very high sound quality, a lot of square dancing on the street to get a set of the kind of on the line, it is estimated that may be a thousand dollars.