At present, probably not, but mobile phones are not 100% secure1, and there are a few minor situations where your location could be guessed.
There are two particular situations where your location could be given to a complete stranger: accessing gyms, or otherwise allowing a stranger to access your game, directly.
It is also worth addressing the fact that Niantic Labs confirm that it might be shared, in the future. In fact, you acknowledge and agree to this, when you sign the terms and conditions to create your game account.
When you take over a gym, your player icon is shown, above the gym. If we were to make the assumption that you happen to pass that gym enough to defend it, we could infer that you live/work/go to school nearby. We could assume that we would run in to you, by frequenting the area. If the assumptions are true, the user would still have to deliberately know your username, in order to specifically identify you as the trainer.
As previously mentioned, if a user is watching the gym as you take it over, they would be able to assume you were within close proximity. Your proximity circle extends to 40m, so that still gives them a 80m area to work with. It would be especially difficult to locate you in a crowded area, and this is not really an issue you should be worried about.
Accessing your game directly through your phone
While outside the exact context you provide, if a stranger was able to physically obtain your phone and access your game, they could see some of your location data.
Whenever you catch a Pokémon, the location is saved, and is view-able when you select that specific Pokémon. If a stranger picked up your phone, and looked at your Pokémon locations, they would be able to determine locations where you most likely frequent. If we assume that you would most likely have one or two Pokémon caught near your house, you can see that this might have the potential to cause concern.
Even with the small chance that somebody would pick up your phone, and even think to access your Pokémon locations, there is a simple solution. If you have any concern of this happening, simply lock your phone with a pin or password. You also want to consider that your overall objective is to not lose your phone, in the first place, and that other applications you use may be more dangerous in the same situation, to begin with.
Last Updated: July 1, 2016
2. COLLECTION AND USE OF INFORMATION
ii. Gameplay Information.
"During game play we will collect certain information, such as your (or your authorized child’s) user name and messages sent to other users. This information will not allow others to identify you (or your authorized child) unless you (or your authorized child) choose to use your (or your authorized child’s) real name and other identifying information."
e. Location Information.
"The App is a location based game. We collect and store information about your (or your authorized child’s) location when you (or your authorized child) use our App and take game actions that use the location services made available through your (or your authorized child’s) device’s mobile operating system, which makes use of cell/mobile tower triangulation, wifi triangulation, and/or GPS. You understand and agree that by using our App you (or your authorized child) will be transmitting your (or your authorized child’s) device location to us and some of that location information, along with your (or your authorized child’s) user name, may be shared through the App. For example, when you take certain actions during gameplay, your (or your authorized child’s) user name and location may be shared through the App with other users who are playing the game. We may also use location information to improve and personalize our Services for you (or your authorized child)."
1 For two examples, Facebook will (by default) log your location, and submit it with messages. If you message anybody with geo-tagging enabled, they will be able to view your GPS location at the time of sending the message. So will anybody that later views the message on your side, including you. In contrast (in terms of difficulty), the Samsung keyboard app had a security issue that has since been found and fixed. As a result, anybody could access your phone through a fake application update, and have access to anything on your phone - including your location. Nothing is 100% secure, in computer application, but common sense is usually your best protection.