Well, yes and no. Every 6 dB you decrease the level means loosing a bit. So, if you feed your sound card at -24 dB, then you actually have 12 bits of audio of the 16, and using 24 bit mode would help. Similarly, using more than 16 bit for input can be slightly beneficial if you want to boost the level REALLY a lot, for example if you boost classical music by 30 dB in quiet parts (you probably wouldn't want to do that, by the way, but as an example).
In those cases, using 24 bits would lower the noise level a bit. However, the noise gate will do something similar, and you can also still use the Dequantizer if you really want to do some crazy stuff
