If the belt is rubber, the friction is high enough, even when the system is starting from zero. (Assuming pulleys shaped like the ones linked above, of course.)
Whether a frictionless pulley is useless or not depends largely upon whether you are using it to change the direction of the line, adding tension to it, or using it to perform work. Such a pulley is only useless for the latter, such as a belt turning a drum, but a frictionless block and tackle or tensioning pulley would be incredibly useful.
