From my own research (YMMV) I think that it does work (but I haven’t used it myself) but just like pharmacy antibiotics it destroys the beneficial bacteria along with the pathogenic.
While often said to be ‘less effective than penicillin’ it works (as I understand it) via the oligodynamic effect:


Currently silver preparations show some effect against antibiotic resistant bacteria, though it is believed that it is possible that bacteria may develop resistance to silver if it is used as much as conventional antibiotics.
Just like conventional antibiotics, C.S. has little to no effect on viruses as they don’t rely on metabolic pathways which the silver can disrupt.
Taken internally (for a prolonged period of time) there is also the risk of argyria if the solution has particles that are too large in it.
It is a hospital recognized treatment (Externally) for burn management and healing.
It can be made at home with basic equipment, or made better with some moderately involved circuitry to regulate the amperage of the current that is flowing (more than a cellphone charger will).
The single most important thing to remember if making colloidal silver to take internally is to ONLY use distilled water and NEVER add anything to the production vessel except the water and silver.
Some internet authors advocate adding salt – this increases the conductivity of the solution and speed up the electrolysis of the silver used, but also forms larger silver salts that will quickly cause argyria, and potentially liver and kidney damage as they are too large for the body to excrete.