Now that you mention it, I would also guess that if the right Aes Sedai found out, the written non-Black liar would be sent to the Amyrlin for penance and made to understand the error of their ways.
I don't think it's ever explicitly mentioned.
However, from what we know of the Oaths, it might depend on the Sister's interpretation. If she believes it includes writing then it would. This is likely the default belief in the Tower. If she could somehow completely convince herself that it...