On Linux, the OOM reaper should come for the memory cannibal eventually, but it can take quite a while. Certainly it’s unlikely to be quick enough to avoid the desktop going unresponsive for a while. And it may take out a couple of other processes first, since it takes out the process holding the most memory rather than the one that’s trying to allocate, if I recall correctly.
Unfortunately, modern web browsers are horrible pigs. No matter what distro you put on this thing, interacting with webpages will be s-l-o-w. (I have a similar laptop—2 GB RAM, Athlon64x2 CPU—running Gentoo, and while it’s functional in its primary job of “larger-screen video iPod for 720p or less”, starting a browser takes a while.) The niche your friend wants to make this machine fill is about the worst one possible for it.