Calling from a landline (or anything that you can't move without a lot of effort) will always give extra information such as where the phone is located (if you've ever signed up for landline service you entered this in somewhere, carriers are required to record it). Some even have specific information, like "3rd floor west stairwell at [address]", but that's only for public buildings. I'm sure you could call 911 and give them a heads up if you had a reason to believe you might call in the future, though. Office phones usually have a office number or at least a hallway (this is why calling 911 from a VoIP phone has a delay, it needs to route you through a real phone number with this information, and Cisco's solution for that is really slow).
A lot of areas have the ability to query a cell phone for its location, but it depends on how much that city/county/state(?) spends on 911. It's usually based on carrier location (so it's not really that helpful anyway), and calling from their phone probably won't help much since you're both in the same location. Caller ID might help if they have a recurring problem (like if they have epilepsy or something that the medics that show up would need to know), but for a concussion it's pretty unlikely they had called 911 before so it probably wouldn't have done much. I remember reading something about iOS sending medical cards somehow when you call 911, but I don't think that's a feature yet (and it relies on iOS, so if they didn't have an iphone it wouldn't help anyway).
Source: I help test emergency boxes (the things with the blue lights in parking lots), landline phones, and cell phones at my job every year. I have to confirm different info based on what I'm calling from. On cell phones, it's just the number the call is being made from. By the way, if you're wondering, 911 does not appreciate hundreds of test calls being made unannounced over the course of a day. We do it anyway :^) (we're required to)