Improv

Today, I was doing a monologue as Joan of Arc and got a friend to stand onstage with me and sentence me to death.  It was a performance, and while I had rehearsed, I had never rehearsed with him, and as far as I know, he didn't know the play.  As such, he had to improvise his actions and reactions.  In this particular monologue, Joan spends several lines begging for mercy, accusing her accusers of wickedness, and touting her own virtue.  When she sees that her accusers are unmoved, she changes her tack:
"Then, Joan, discover thy infirmity,
Which warranteth by law to be thy privilege:
I am with child, ye bloody homicides!"
I began that last line quietly, and increased volume until I was yelling the word "child" at my friend.  He was visibly startled: his upper body jerked back, his eyes widened, and his mouth dropped open.  A perfect reaction, and completely organic. 
What I'm wondering is this: do you think improv has a place under the heading of art?  Is it more of a craft?  Is it too closely related to simple, cut-and-dry life?  Does its close relation to everyday life keep it from being art?

Lines from Shakespeare's Henry VI, Part I