Otherwise I think it depends a little on the server - but if it's expecting a standard HTTP POST then it shouldn't be too hard (I just don't think anybody has asked this so far).
Having said all that I imagine that unless you're very careful you're probably going to hit speed limits in Espruino itself, not your access point :)
Espruino is a JavaScript interpreter for low-power Microcontrollers. This site is both a support community for Espruino and a place to share what you are working on.
So you want the Espruino to upload to a webserver, or you want Espruino itself to be a webserver, which accepts file uploads?
If it's the latter then there's some code available for it here: https://github.com/espruino/Espruino/issues/226#issuecomment-181443491
Otherwise I think it depends a little on the server - but if it's expecting a standard HTTP POST then it shouldn't be too hard (I just don't think anybody has asked this so far).
Having said all that I imagine that unless you're very careful you're probably going to hit speed limits in Espruino itself, not your access point :)