Its definitely possible. Had one fallen in love wit me after a month b4.
I had doubts that her feelings were sincere, so I asked her. I asked her how does she know she was truly in love wit me. She pretty much told me it was my personality...how I viewed things regarding relationships...how I treated her. Also how she saw that I could be husband material.
If a guy gets all the check marks on what that woman is lookin for in a man, and they're just starting out, then yeah...its possible for her to catch feelings/fall in love quickly.