He's going to let it evaporate. The acid in vinegar is called acetic acid. This acetic acid is what gives it it's characteristic vinegar taste and smell. Acetic acid is what we call a volatile acid. That means that it evaporates into the air. There won't be any left in the reed when it has evaporated. All the acid will be in the air. The reed won't taste of vinegar because there won't be any vinegar in it or on it. It won't hurt the mouthpiece or ligature because there won't be anything left in, or on, the reed to hurt them.Certainly it will make the reed taste of vinegar -you may like this or not, plus the vinegar will possibly damage hard rubber and metal plating on mouthpieces and ligatures
Having said that, I would advise using distilled spirit vinegar, which is effectively a dilute acetic acid solution, because wine/cider/malt and especially balsamic vinegars contain other substances that you probably don't want in your reed.