Depending on the pitch of the prop, it may produce relatively little "pull" when stationary relative to the airflow, and a lot more as it reaches optimum. So you may find you get better acceleration from the prop as you approach Vr. Variable pitch props help a lot here!
I thought about that as was writing Keef, and even changed my mind and my text a few times! On reflection, I think I'm sticking to my story.
Though the efficiency of the prop gets vastly better with speed, the thrust does not. It's true that some very coarse fixed pitch blades may be stalled at low speed, but I don't think you have to be going very quickly for them to unstall themselves. From what I can see from the charts I have, you need to be getting into the 30+ degree pitch before there is any increase in thrust coefficient with advance ratio. Everything less than that shows a monotonic decrease in thrust coefficient.
So I think you're always going to be losing thrust as you accelerate.