Hi Jason,
In broadcasting, you usually mix your audio to what your video tape editor requires. So that means you will mix your audio and or dither it to what your Digital Betacam Editor expects, which of course is 20-bit digital audio.
If you feed 24-bit audio to a machine that expects 20 or 16-bit depth, it will probably get recorded in a way that sounds awful. (Too much resolution for the design of the machine.)
If you dither 24 bit audio down to 20 or 16-bit, what you are actually doing is adding white noise to the sound (hiss in other words.) 16 bit will have added to it more hiss than 20 bit audio, but in all honesty, most people will not notice it. If you import a 16-bit audio into a 20 bit mix, you will not be subtracting any hiss the audio may already contain. But some sound engineers have explained to me that when you mix in 20-bit mode, the 16-bit audio will playback with less hiss (less hiss caused by white noise.)
16-bit audio playsback as 16-bit until it is mixed to 20 or 22 or 24-bit audio. Then it becomes 16 bit audio inside a higher bit depth audio envelope.
It appears the decklink cards are only 16-bit audio, but that will need to be confirmed by BMD.
Regardless, it is better that you dither the audio in a sound program than have a computer card do it for you on the fly.
(ON the other hand, if the DeckLink card does not dither the audio, then it will just output whatever is fed to it, causing your Digital Betacam Recorder to record digital audio harshness if the audio is not 20 or less bits per sample.
Hope this helps,
Paul Thurston