I'm saying that I think it would help. I've recorded my swing, and often when I putt I'm moving the putter away from me. It's something that I have to learn to not do, and I'm assuming that if I had an anchored putter I would probably not do that so much. It's an assumption.
It may just be how the putter is fit to you. I had a similar issue before I got fit. When I started to draw back the putter, it moved away from me about 1/2" or more at the start instead of moving back along the arc. After I got fit, the length was increased 1/2", the lie decrease quite a bit to 68 deg and the loft to 5 degrees. This allowed me to have the putter in the proper position for my stroke. My aim improved as well.