Yes. You can do this. First, watch this video for how audio works in iMovie.
Then watch this video on how iMovie 11 audio has additional features.
Click on the video that is names "All New Audio Editing"
Those two videos will give you the basics.
For your specific question, you will drag in your music track and drop it on the slide where you want it to begin, so it shows up as an audio track under the slides rather than as a background audio track. Then you can drag the right edge of the track to the left to shorten it, as in the first video above.