http://www.troyhunt.com/2014/10/find-crazy-stuff-in-mobile-a...
"Here’s a pop quiz for you: how much data do you reckon this iPad app downloads when it first runs? I don’t mean how big it is to download from the App Store (it’s 25MB), I mean after you download it then simply tap the icon to fire it up, how much data does it pull down if you don’t touch it again? ... Try 1.8 gigabytes. You heard me, that’s not a typo. You open up this 25MB app and it’ll pull down dozens of files of dozens of meg each when you run it. Won’t someone please think of the bandwidth!!!"
There is nothing with Ajax that does that automatically or even by default.
With the favicon issue these things don't happen.
Mind you I'm sat at home with a 300Mbps fibre connection, so I don't give as much thought to bandwidth as a roaming 4G/3G user might.
Web workers will not show a loader indicator however. You could probably do a nice DDoS attack like this even. But it requires users to be on your site anyway. Might as well just stick 0day du jour on it.