Nor can your Clip+ really. It converts everything to 16/44.1. In the recent development versions Rockbox on the Clip+ can be switched between 44100 Hz and 48000 Hz sample rate. Every audio track of a different sample rate gets sample rate converted using a simple rate converter without anti-aliasing.
Loading your Clip+ with 24/96 is a complete waste of disk space and time. You would be much better off to use a good quality sample rate converter on PC to convert the audio to 16/44.1 and then load that on to the Clip+.