The main feature of the suggested buffer is to intrinsically limit the signal swings so as to not exceed +5V, or go below ground, on the A/D, since many such parts will go into latchup under these conditions and self-destruct. Also, it provides +6dB of gain, owing to the complementary outputs, which may or may not be what you want.
Wavefront is not clear in their datasheet about the consequences of exceeding the rails. But their "single-ended input conditioning circuit" shows unspecified opamps. These could I suppose be rail-to-rail output swing low voltage parts run from +/-2.5V, but of course the B*hringer schematic from gyraf shows high voltage amps. Maybe the Wavefront part has protection against latchup. It is frankly odd, and suspicious, that there is no Absolute Max ratings table.
Note that even with r-to-r limited to 5V a coupling cap can produce voltage excursions with low-frequency square wave drive above and below the rails of the 1101. The buffer will do this too without the protection diodes. But that would be an extreme signal.
Certainly you can take advantage of the diff. inputs of the 1101 and drive them directly, if your source Z is reasonably low. The spec on input Z for the 1101 is 160k differential, and each input is internally biased to half Vcc, i.e., 2.5V.
I'm suspicious as well of the common A and D ground claim, although it is more feasible given their differential inputs.
The details of the clocking requirements are given in the datasheet ("2s complement serial data in a standard MSB-first format.")