If my wife does not testify against me in court will I be convicted of aggravated assault under the family voilence act?

It depends on the facts of your case.  Without her testimony the case will not be as strong; in fact if the case rests soley on her testimony, there is essentially no case at all.  However if there are such things as other witnesses, physical evidence of the assault (pictures of bruising, etc), and the police report you could still be convicted.  It's happened before.

It should go without saying - do not threaten or intimidate her in any way.  You will be committing yet another crime and the DA will be only to happy to file charges against you for that as well.

You need to speak with an attorney in your area on all of this.

Although I do not practice law in the State of Georgia, here are my initial impressions.  First, in any criminal proceeding, it is the state's burden to prove the defendant is guilty "beyond a reasonable doubt."  Thus, the state must rely on evidence in order to do this.  Your wife's potential testimony is only one example of potential evidence that may exist.  To answer your specific question, if the state's case relies solely upon your wife's testimony, then it is unlikely that the state could obtain a conviction without her testimony.  However, if any other evidence exists, then conviction remains a possibility, and depends on the amount of and quality of the other evidence.  It is also important to remember that your attorney may be able to preclude your wife from testifying pursuant to the marital privilege.  Nevertheless, you should not proceed forward until you have consulted with and/or retained an attorney to discuss the strength of the state's evidence, as well as the merits of any and all potential defenses that may be available to you in the interest of obtaining the most favorable resolution of this matter as possible.