Are the subordinate genes of a repressed operon really "turned off"?
There are several mechanisms by which the expression of a gene can be completely turned off. Certain network architectures can ensure foolproof repression (for e.g. by using multiple repressors parallely or additional epigenetic silencing mechanisms). Bistable switches can also ensure robustness of expression in a way that small fluctuations in the transcription factor levels do not lead to expression of the gene. Sometimes the activator molecules need to co-operatively activate the expression. In such conditions the activation graph is sigmoidal with respect to activator concentration. All these mechanisms can prevent leaky expression. 

Some genes do have a basal expression but it is not necessary for all cases. However, basal expression is absolutely necessary for proper functioning of the lac operon (see this post). 

Having said this, there is always some non-zero probability of expression of a gene when it is actually turned off. This probability may be very low but it would not be zero. This small accidental expression may or may not have any significant downstream effects.