No, we cannot conclude the surface tension to be zero solely by the fact that the liquid neither rises nor falls in a capillary.The height of the liquid inside a capillary tube is given by h=rρg2Tcosθ​ . From the equation, we see that the height (h) of the liquid may also be zero if the contact angle  θ  between the liquid and the capillary tube is  900 or 2700 .