If it is forbidden to speak God's name in vain, and it is forbidden to desecrate God's name in the writing of any language (MB 85:10), then it seems obvious that it is forbidden to irreverently sign God in conversation. The simple idea is about the respect we give in referring to our Creator.
Nevertheless, if you wanted to look down the pilpul glass, then it's important to note that the issue of determining the status of sign language as a halakhic language is an evolving one. This question has particular contemporary significance for the religious participation of deaf people. A good introduction into the changing status of how halakha understands sign language is a responsum written last year by R. Benjamin Lau on conducting weddings for the deaf. He argues that the advances and sophistication of modern sign language perforce changes the status of deaf people from that of feeble-mindedness, as understood during the Talmudic Era, to that of intelligence. In doing this, R. Lau argues that sign language should now be considered a full language, and he quotes other authorities who agree with him (such as Chief Rabbi of Israel David Lau) and those who do not consider sign language a natural, normal language (R. Yaakov Ariel).
So at the moment, while there is not a consensus as to the halakhic status of sign language as a language, it seems to be evolving toward greater recognition. Perhaps this prevents us from answering the question (although I still believe the spirit of the halakha should be accounted for here).
P.S. As someone who studied sign language, I personally find that it completely parallels speech in terms of communication. In ASL, the word God is, like spoken English, a general term used by many kinds of religious and secular people (as opposed to the Jewish term HaShem). In Hebrew sign language, the word for HaShem is made pointing the index finger upward toward the sky. This recalls the signing used in the Talmud (Br. 48a):
אביי ורבא הוו יתבי קמיה דרבה, אמר להו רבה: למי מברכין? אמרי ליה: לרחמנא. - ורחמנא היכא יתיב? רבא אחוי לשמי טללא, אביי נפק לברא אחוי כלפי שמיא.
Abaye and Rava, when they were children, were seated before Rabba. Raba said to them: To whom does one recite blessings? They said to him: To the All Merciful. Rabba asked them: And where does the All-Merciful reside? Rava pointed to the ceiling. Abaye went outside and pointed toward the heaven.
