Is an annulment possible if my husband and I own nothing together and have never acted as a married couple?

The grounds for annulment are very specific impotence or some fatal legal defect to the marriage that renders it void (like bigamy, incest, one person was a minor, or some other legal prohibition to the marriage). The statutes that set out what marriages are void are N.C.G.S. 51-1 to 51-5. If you have a living child with the Husband, then the statute specifically prohibits annulment. If you have one of the requirements for an annulment that are listed in the statute, then you have to file a lawsuit, go to Court, have a trial and prove your case. It is time consuming and expensive plus, after all that time and expense you can actually lose and end up having to go get a divorce anyway. It is almost never worth the time and the money to try to get an annulment. A divorce is almost always the faster and more certain approach to terminating a marriage. Not living together is not one of the grounds for annulment.