If you play back at a high enough level, hearing the difference is quite theoretically possible. The human hearing has a dynamic range of about 120db, which is what 24 bits has, so there is no wonder 24 bits may sound better.
However, CD's are still 16 bit, so in that sense it won't make a difference, because you have to throw away the extra 8 bits anyway. Therefore, 24 bit recording will not in itself make an imporvement on the final product. It does give you 8 extra bits (24db) of headroom though, so you don't have to watch your levels. It also enables you to compress after recording without loosing as much detail as compared to compress before recording as 16 bit would.