Yes and no. A toilet with no vent may not flush the contents out of the bowl, but any other drain will work without a vent. (NOTE: the code is that all fixtures shall be vented). In my experience, only twice in 15 years has a vent been the cause of a drain backup. In one case it was roofers who stuffed the old roofing material down the vents and the other was just a stray piece of wood. In both cases the material made its way down into the drain pipe and had to be removed. No amount of vent cleaning would have done any good.
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