I am very peculiar about mouse sensitivity and have not seen Action! have any negative effect on my mouse input in 3 years of using it across various game.
The only thing similar to what you are talking about are FPS drops due to the added resource usage that affect mouse input like so:
What I suggest is that you enable AMD APP / NVIDIA CUDA rather than using your CPU to encode the videos you capture, that should minimize the performance hit. Also look into disabling mouse acceleration to get a consistent mouse input and the ability to measure your sensitivity via 360/cm or 360 or 720/mousepad width