Sure. But it will do them little good, as you need your body-weight behind the racquet (in other words holding it) to redirect the ball back into the oppositions court.
And I believe there is a matter of a "misconduct fine" imposed on the "thrower" so, as long as you are willing to pay that (say $5 - 10,000.00) for the infraction; go ahead and toss it. I am of course referring to professional play.
Yes, you can. If you have an arm and a racket it's possible. But of course there will be some 'fallout'. If it's a casual game with a friend you may loose a pal. If your playing in a real competition you will probably be asked to leave the court. As in the case of McEnroe and Wimbledon, you will be asked to leave and not return.
So it all comes down to choices and consequences. If you don't care if you are in good standing with the rest of the world, by all means, throw that racket.
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No, it is physically proven that a human is unable to go through a tennis racket.