Can I sign divorce papers in my husband's name if I have general power of attorney?

Tough question.  It is hard to answer without knowing why you have a general power of attorney for him. It would depend on your state laws.  Usually, someone with a general power of attorney can sign things for the other person, but has to act in the person's best interests - fiduciary duties.  I have not researched the issue, but I believe many courts would hesitate to enter an order affecting his interests if it is only signed by you - the party who can benefit significantly by signing for him.

In Washington, to make sure the divorce is final, I would either have the husband sign if he has not been declared incompetent, or ask the court to appoint an attorney/temporary guardian to determine husband's competency and possibly sign for spouse.  You want to make sure it is done right and final. 

From a practical standpoint, if he's competent, I would file and have him served and if he doesn't respond, get a default order and enter your final divorce papers. If you don't know where he is, you could serve him by publication.