It makes sense for Andrea's character to take the path she's currently on. She's lost everyone she's loved, come close to suicide several times, and doesn't even know what the believe in anymore. Michonne referred to the Governor as a "Jim Jones" type last night and it fits 100%. He's giving Andrea a false sense of hope and to her it's the greatest thing she has right now. She thinks she's safe and now has many people in Woodbury who will care about her, especially the Governor.