A separation agreement is designed to keep from going to court over custody, equitable distribution, and child support. You can file for divorce if you have been separated for one year and one day. A separation agreement or lack of does not affect your eligibility to gain absolute divorce. If she signed the agreement then she is legally bound to it, unless she wants to take you to court and fight it out and even then, most cases a signed agreement holds up as long as it’s fair.
If the alimony has already ceased due to cohabitation as stated in the separation agreement then there is no reason to restart it after divorce. Below are the laws on alimony but since alimony was not court ordered in your case, she would have to take you to court, get alimony court ordered and then show that she has not already violated that order by cohabitating.
“An order of postseparation support will terminate, pursuant to the applicable statute, if (1) the parties resume marital relations; (2) the dependent spouse remarries; (3) the dependent spouse cohabits with another adult in a private heterosexual or homosexual relationship; (4) the dependent spouse dies; or (5) the supporting spouse dies.”
“Any motion to modify or terminate alimony or postseparation support based on a resumption of marital relations between parties who remain married to each other shall be determined pursuant to G.S. 52-10.2.
(b) If a dependent spouse who is receiving postseparation support or alimony from a supporting spouse under a judgment or order of a court of this State remarries or engages in cohabitation, the postseparation support or alimony shall terminate. Postseparation support or alimony shall terminate upon the death of either the supporting or the dependent spouse.”
I would say you are in the clear to file for divorce, include the signed separation agreement and move on with your life. It’s possible that she could answer your divorce complaint with some issue about the equitable distribution but that will not “hold up” the divorce.