If tea has gone bad, then it will be obvious from the smell or mold growing on the surface of the tea, so most likely, you will not even drink it. If someone does sip it, it will also taste sour, so they will probably not drink anymore. Old tea can contain coliform bacteria, which can cause symptoms such as diarrhea, nausea, and vomiting. So yes, old tea can go bad and make you sick.