No, not in the headphone jack. It would have to be someplace viewed easily. As stated already, it's on the battery itself, and it doesn't have to be a solid dunk in water - it can slowly turn from white with red dots/x's on it to a light pink, and more red as the phone is introduced to repeated high humidity. As a VZW rep for our military recruiting team a few years back, we saw a lot of battery indicators turning light pink and then darker over time before polling the users. The general consensus was that most of the time those that carried their phone in their front pocket incurred the quickest turning to red based on the higher moisture content. If you don't have a belt clip, use your back pocket, jacket or upper shirt pocket, or purse if female.
Ciao,
JT