Activated carbon removes a lot of chemicals, especially covalent ones (hydrocarbons). Examples of compounds that are removed with high efficiency with carbon: benzene, decane, oil-based pesticides, the components of diesel fuel.
Ionic compounds, including all salts, are so soluble in water and lack hydrocarbon structures that will bond to the carbon, therefore they will adsorb weakly if at all onto carbon. Examples include sodium chloride (salt), sodium bicarbonate (baking soda) each of which is quite safe, but also sodium arsenite, a gram of which could kill you.
Other compounds like alcohols are in between. Small, simple alcohols (methanol, ethanol) don’t adsorb much at all, but as the hydrocarbon chain gets longer, they adsorb more efficiently.
And, yes, I’m using “adsorb” because it all takes place on the surface of the activated carbon, not absorbed into the bulk of the carbon. The carbon is usually a charcoal derived from coal, almond or coconut shells.
So, if you’d die of dehydration otherwise, obviously drink it. If you treat it with a filter, chlorine, or UV, you’ve rendered it safe from an infectious disease perspective, only. Activated carbon would remove some but not all chemicals dissolved in the water. A majority, I’d say, but not the vast majority of toxic chemicals.
You could grab a sample and run a few hundred dollars of tests but that would leave a lot of unknowns (because you don’t what to look for). A few thousand dollars and you could be pretty sure.
A cheap DIY test would be the home version of a “wet test” in which the lab puts trout fingerlings (they’re more sensitive than the carp family) in the sample water and compare their survival to another population in known clean water*. 19-cent goldfish are cheaper and more readily available and would tell you if the stuff was more acutely toxic.
* for protocol reasons, they can’t reuse the trout fingerlings after a wet test, so the last one I had done, I asked for the fish that survived and kept them on my desk at work for a few months.