No, it does not. For one, Shadowplay does not do any scene compositing, because there is only one "source", so it does all of its work directly on the GPU without having to move data between the GPU, RAM, and CPU. Second, Shadowplay, being an NVIDIA product, has access to hidden NVIDIA API functions that are more efficient than what they make available in the public APIs for NVENC. Shadowplay will
always be more efficient than other recording applications because of these two points, but it is far less flexible and powerful in what you can do with it.
In your case, you running Overwatch at its current settings and OBS is causing your GPU to become incapable of keeping up with demand, causing render lag. It's taking just a bit too long to get the rendered frame from the GPU. This is most often easily resolved by capping your Overwatch FPS to your monitor's refresh rate, especially if your monitor is 60Hz. You can also disable the Windows 10 Game Bar and Game DVR, which may reduce load slightly. If that does not resolve it, please post a new log file after trying that.
Please also download
GPU-Z and post a screenshot while a game is running or while using the app's render test (the blue question mark on the right side). Use the camera button in the program and upload to free image hosting.