Akamai's configuration is highly configurable, but normally, you can define what type of content you want to store, and for how long (on Akamai's network and on the user's browser). Akamai also has a multi-teir system, so that if a users makes a request from a local Akamai server, if it doesn't have the content, it will request it from a parent tier. If that parent doesn't have it, the parent tier will request it from the grandparent tier. After that, the Akamai grandparent tier would from request it from the origin. Once it pulls the content and sends it to the user, it will store it in cache (at every tier). Any subsequent requests are handled by the Akamai network. If that content not requested again, it's purged from the cache eventually. If it's a busy Akamai server, unused content will get purged quicker than if it's not as busy.
I don't believe that Akamai has the ability to store user content on their servers, their network is not designed for that. When you upload an image to Facebook, you're uploading it to Facebook's server (I remember reading a whitepaper on Facebooks custom filesystem to handle image requests).
On a normal website, Akamai could take up to 95% of the traffic off the origin, depending on configuration. On something like this, I don't think it'd be as high, but any percentage would help.
At first thought, I would assume that Akamai wouldn't be able to help much, a normal users profile elements are not accessed enough to make a difference. But as I think more about it, if you're pretty popular user in your area, having your pictures cached on the local Akamai server may help when other people accessing your FB profile thru the same local Akamai server.
The real benefit of using Akamai would be on a celebrity's page, or a companies page, or just the static elements (css/js) of Facebook's site. Anything of high volume
So, given all that, my assumption is that for normal user's profiles, when you upload them to Facebook, they're stored on Facebook's servers. When you request them, Akamai goes back to Facebook's origin servers, pulls them and puts them into cache. If your neighbor goes to look at them, they'd be on the same ISP (ideally) and would pull them off the Akamai cache server that resides (ideally) in your ISP.
All that being said, I know nothing of Facebook's Akamai configuration, so they may have something completely custom and outside the norm.