In "ideal" conditions with proper nutrients in the water and depending on the bacteria, then yes. In a lake, or any ecosystem, a balance gets developed between many different species. So the bacteria are kept in check by protozoa, algae and similar microorganisms all competing for the same food (nutrients) and there are various species that have defenses against each other. There are bacteria everywhere -- millions of them on even a small patch of your skin. The problem isn't in having lots of bacteria, the problem is having lots of the WRONG bacteria (or protozoa or viruses).
In pool water, the wrong bacteria is usually that associated with fecal matter. This includes various common strains of E.coli but also includes pathogens associated with disease including viruses. Though it's not a pleasant image, you really have to think of an unsanitized pool as a toilet bowl (whereas a sanitized pool is clear and clean water). In a lake, river or stream, the various organisms tend to self-clean or at least keep in balance what is dumped into them, but they can certainly be overwhelmed. For example, cholera is caused by a bacterium and can readily be spread even in "open" waters as this was a real problem in India (most people know about the "wells" in England, but those were not open waters). There's an interesting account of this and other cholera outbreaks at this link.
The reality is, however, that the risk of getting disease from even an unsanitized pool is low. It's just that sanitation reduces the risk to near-zero, at least for the easy-to-kill pathogens that low levels of disinfecting chlorine takes care of. The biggest risk in an unsanitized pool is transmission of disease from person to person which is why most serious outbreaks are in commercial pool environments where there are heavy bather loads (i.e. lots of people) rather than residential pools. In a residential environment, the most common problem is with hot tubs where the bacterium that causes hot tub itch is not uncommon and takes somewhat higher levels of chlorine to kill (so using Dichlor exclusively in a hot tub is not wise, even though that is often recommended by the industry).
Richard

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