| Assuming your powered speaker is designed to accept speaker-level inputs, and your alarm clock speaker is of the same impedance as the input to the speaker (the alarm probably has a cheap 8 ohm speaker in it), then you should be good to go.
The only thing I can think of off hand is if the circuitry inside the alarm isn't fully isolated from the line voltage (can't think of a reason it wouldn't be, though), you could have a problem there.
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