Yeah I played with it a lot, its definitely possible. Adjusting the transfer rate definitely shifts the frequency around. I'd planned to hook up the system to a preamp, then record the power spectral density of the noise at various transfer rates.
I assumed that the noise is the result of mixing in the amplifier between the SD clock the SD bus. Presumably we could work out a model such that a lot of the noise can be shifted out of the audio band to higher frequencies. I haven't gotten around to it yet, and its kind of annoying since I don't really understand the SD driver yet.