Does any game make use of the Game Boy Serial Data Pin?

The Game Link Cable

The most obvious candidate for this are games that use the Game Link Cable. Individually checking all of them would be an imposing task, but luckily we don't have to. A schematic drawing of the wiring of the 8-bit Game Link Cable shows us this:

Plug 1         Plug 2  
 SI ______  ______SI  
 SO ______><______SO  
 GND_____________GND  
 SC _____________ SC  

There is no wiring for the SD pin. From this we can conclude that no games using the standard Game Link Cable will make use of this pin. This also rules out the Gameboy Printer and the four player connector as both connect using a standard cable.

Other Candidates

This leaves us with more specialised hardware that connects using the Game Link port but does not use the Game Link Cable. Apart from the unreleased Work Boy there are only two options:

Game Boy Mobile Phone connector

Released in Japan only for use with some Pokémon games.

Singer Izek 1500

An Game Boy-enabled embroidering machine. It has a built-in custom link cable and a custom game cartridge. The Game Boy is used to select different patterns and options.

Sadly I don't have access to either piece of hardware and thus can't tell what pins they use.