Was there ever an a cappella version of Nemurihime released?
An a capella version of this song has not been released yet.

According to VGMdb* and imas DB, Nemurihime was only ever released on two CDs:


THE IDOLM@STER MASTER ARTIST 2 -FIRST SEASON- 05 Chihaya Kisaragi: This was the original release of the song and therefore is not a special version.
THE IDOLM@STER ANIM@TION MASTER 07: This is one of the many soundtracks for the anime series, but it is still the original version and is not a capella.


Note: Neither referenced site has an official relationship with the iM@S series, but they are both reliable fan-made databases.

Since the airing of the anime, Nemurihime was also released on DVD/Blu-Ray of live performances on:


THE IDOLM@STER 7th ANNIVERSARY
THE IDOLM@STER 6th ANNIVERSARY


However I looked up the videos of these performances and they were both the original version. I think it's safe to say that any performances of Nemurihime before the anime are also the original version.

* Since VGMdb does not have permalink search feature, these are the parameters I used:


  trackname -- 眠り姫
  game -- idolm@ster