That depends on what the condition is, how trustworthy the anecdotes are and how much someone was trying to charge me for it.

For instance in the case of terminal cancer, some people get ripped off by charlatans to the tune of hundreds of thousands of dollars. The anecdotal data around these assholes is all overwhelmingly positive and claims no side effects, because people who are ripped off and then die tend not to talk about it but the very few who survive for reasons unknown shout a lot. The reason you might not try it is because you'd be bankrupting the family you're going to leave behind, or funneling good-will donations to a conman.

There are numerous examples of alt-med 'cures' that are dreadfully harmful (black salve, sodium hypochlorite enemas). This idea that CAM is fine to try if you're out of options because it has no side effects is itself very dodgy. Hell, even acupuncture carries some elevated risk of infection because you're pushing needles through the skin.

But if it was something minor, cheap and there really were no side effects, sure - why not?

--edit-- But telling if there really are no side effects does require some basis in provable fact, or you're just necking unknown quantities of unknown stuff, which may not be a great plan.