Recent versions of gPXE have support for booting over wireless, but the wireless connection model (where you might be moving around and have a weak connection s

Recent versions of gPXE have support for booting over wireless, but the wireless connection model (where you might be moving around and have a weak connection sometimes) isn't very amenable to having your root filesystem mounted over wireless. You also have to do more setup, partially because the wired discriminant of "use the network attached to the cable that's plugged in" fails. So, it's definitely possible, but it might not yet be worth the effort.