It depends pretty much entirely on how you define "conspiracy". Eg "conspiracy to commit murder" (or election fraud or something, more topically) doesn't require secrecy at all (except in order to be successful, maybe) while "conspiracy theory" (when it's not being abused to the point of meaninglessness to dismiss legitimate accusations) is specifically based on the implausability of many thousands of people not just keeping a secret, but concealing any evidence that there even is a secret.

Plenty of things are conspiracies in the "conspiracy to commit murder" sense, without being conspiracies in the "conspiracy theory" sense.