Recent models for the emission clouds within the Broad Line Region of quasars suggest that they are due to transient overdensities within an overall turbulent medium. If this were the case, the broad line emission would spatially appear fractal, possessing structure on a range of scales. This paper examines the influence of such fractal structure when a quasar is microlensed by a population of intervening masses. It is found that while the highest fractal levels can undergo significant microlensing magnification, when these light curves are superimposed to create an emission line profile, the resultant emission line profile remains relatively constant for physical models of the Broad Line Region. It is concluded that the detection of the possible fractal structure of Broad Line Regions via gravitational microlensing is not practical.