Whatever sample rate the mixer is set to is what sample rate the mixer is processing audio at, so that means it affects not just recording, but anything passing into or out of the mixer.
However... whatever theoretical benefits in audio quality that exist for the HD mode sample rates, those differences would not be apparent enough to be useful in a live sound scenario, where the reproduction system (i.e. speakers) and acoustic space are less than studio-quality optimum
The problem is, operating at double the sample rate means almost double the processing overhead, and so some features must be disabled when the mixer is in HD mode (half the FX buses, no Fat Channel on outputs, etc.). Since the benefits to audio quality from using HD mode are subtle, and thus indistinguishable in a live sound scenario, the trade-off in the disabled features of HD mode means using these higher sample rates is intended primarily as a studio-recording-only feature.
There is one possible reason to use HD mode sample rates in a live sound scenario, and that would be if you're using the mixer connected via firewire to a computer and running software plugins as insert effects. Higher sample rates should give you lower round-trip audio latency to and from the computer (assuming the computer has the necessary processing power to make this feasible).
The primary thing that controls round-trip audio processing latency with a computer is buffer size. The smaller the buffer, the less time it will take for audio data to pass through it, therefore the lower the latency will be. With a smaller buffer the CPU has more buffers to process and needs to work harder for smaller buffer sizes to ensure that any delays are kept within the time allowed by the buffer, so how small of a buffer you can run will depend entirely on the processing power of the computer in question.
Because Buffer size remains fixed no matter what the sample frequency is, the higher the sample frequency, the quicker audio data will pass through the buffer and the lower the latency will be. As an example, audio data will pass though a buffer twice as fast when using 96KHz sample rate as opposed to 48KHz.
There still exists the trade-off of disabled features in HD mode, but if the absolute lowest latency when live audio processing with a computer is critical, HD sample rate modes should provide a benefit.