Hello, Karim.
It's not impossible (maybe it was at some time in the past, but not now). What I do is the following. In the Nike+ app, when you select to Begin Run, you're taken to the Run Setup page. There, under the Music setting, select No Music. Press your home button to leave the Nike+ app, then open the Music app. Find your playlist and start playing it (you can even use shuffle, if you desire). Then press your home button and go back to the Nike+ app. You should be back at the run setup page where you can click Start to begin. All the audio announcements/cheers will still play over your music and, as usual, it will lower the volume of your music for the duration of the announcement/cheer so you can hear it.
It's not as nice as having direct access to the playlist within the app, but it does the job just fine (for me). Hopefully, Apple can get this sort of usage worked out (as koreyfromor described above). I hope this helps!