Not in the grown room (too warm) but not in the fridge either.
I used bleach occasionally before I got my chiller (after hot days when frozen bottles weren't enough and) during the weekly refresh. Just a cap in water flushing through the system, then refresh again with only water, they can easily take it.
Nutrient Solution Microbiology
All bodies of water possess a dynamic balance of microbiological activity. In hydroponics, we strive to keep the nutrient solution as sterile as possible [chiller...], but nonetheless, nutrient solution is by its very nature the perfect place for things to grow. Some microbes require dissolved oxygen to live (aerobic), and others do not (anaerobic). As a general rule of thumb, aerobic bacteria are "good," and anaerobic are "bad." Put simply, the by- products of anaerobic respiration are acids that wreak havoc with chemical and biological balances within the nutrient solution, which in turn harms the root system. Warm, stagnant water holds little dissolved oxygen, making it an ideal breeding ground for anaerobic bacteria, many of which (Fusarium, Pythium) cause crop failure as they take up home in the fragile root system and proliferate. The foul smells associated with warm stagnant water (sewers, swamps) is caused by these "bad" bacteria. Methane gas (swamp gas) is a highly flammable "natural" gas that is also a by- product of anaerobic bacteria. Can you see how, left unchecked, these bacteria can ruin a crop? Rampant pH swings, swampy smells, root rot and ultimately crop failure are the tell tale signs of a poorly balanced biology within your system.
Source: How-to Hydroponics (google how-to hydroponics fourth edition, download the pdf, read read read)