A 2x converter on a lens would add 2 stops to the aperture setting so your f5.6 lens would become f11 - clearly that would have an affect on the light getting to the camera sensor and would affect the AF speed of the lens, also it would affect the image quality depending on the quality of the converter.
If there is plenty of light and the converter is very good quality the amount of degradation of image and AF speed might be minimal but in less light the degradation would become more noticeable.