OK, so I finally:
a) Got the ardrone2 stuff working reliably enough that I am not flattening the whole battery trying to get a working link, and
b) Plucked up the courage to actually try a takeoff.
But when I did takeoff, the behaviour was pretty strange - as soon as it was off the ground it shot off at high speed in an apparently random direction, got maybe 15-20 meters that way, whilst climbing, then made its way back to the STDBY point.
Given I have fairly restricted space to experiment in, this was not optimal! Especially since it came within inches of hitting a tree before it started to head back in the right direction.
BTW, the GPS was working fine throughout this, since it accurately traced its weird path.
Any idea what's going on and how I might fix it?