I wanted to understand whether the GPUImageAdaptiveThresholdFilter does automatic thresholding or not.
I'm not quite sure what you mean by "automatic thresholding", but the way that the GPUImageAdaptiveThresholdFilter works is it reduces the image to luminance (grayscale), then performs a box blur on it of a user-defined radius.
For each pixel, the luminance of the pixel is compared to the value from the box blur. If it is higher than the local average luminance from the blur, the pixel goes white, if it is lower, black. Thus, it is thresholding based on the average luminance of pixels surrounding that one.