From the wikipedia page on audio bit depth
Technically speaking, bit depth is only meaningful when applied to pure PCM devices. Non-PCM formats, such as DSD or lossy compression systems like MP3, have bit depths that are not defined in the same sense as PCM. This is particularly true for lossy audio compression, where bits are allocated to other types of information, and the bits actually allocated to individual samples are allowed to fluctuate within the constraints imposed by the allocation algorithm.
So no, it's not a meaningful factor in lossy compression formats. Bitrate and samplerate are the important qualities to look at. I just tried converting a 24b/96k flac file with oggenc, and while the samplerate was preserved, no bit depth shows up in the metadata.
The man page for oggdec shows a bit depth setting for decoding back to pcm/wav, but you can only choose between 8 and 16 bits.