Since SRCTREE-4343 is closed, un-fixed, I'm creating this to bring attention back to this issue. Source tree still doesn't do this.

I've posted the following notes as a comment in 4343, but I'm copying here for the sake of posterity.
 

Yubikey's on mac/linux use the SSH_AUTH_SOCK environment variable to refer ssh to the GPG agent for private keys. Most users run the GPG agent and set this variable in their ~/.bash_profile

Change sourcetree so the shell window opens an actual shell, or at least loads the .bash_profile before running git and it will work correctly with yubikey and other hardware security modules.