No, the arcs don't represent any 'wanderings'
as far as i understand it they indeed do. there was a first second etc... arc - up the the last seventh arc which was last ping with the aircraft - every arc circles other areas. this circles were calculated from a known satellite position at ping time and the time for the signal needed to reach the aircraft but since it was only one sattelite it only represents a circle around the globe and not a fixed position .
the difference in time travel between arrival and return signal - called doppler effect - could say if the aircraft is approaching or going away from the sattelite - and with known satellite orbital path at every ping they were able to exclude the northern corridor.
they were even able to roughly calculating the aircraft speed by doppler effect vs sattelite speed and orbit.
you can surely exclude 360,s since an nearly "stationary" aircraft would be recognized by doppler effect , but - as far i understand it - the cannot say anything about what path the aircraft took between the seven pings , what altitude it had at all and what speed it had between the pings .
realizing we talk here milliseconds in time burst and time offset and the fact the sattelite itself changes its position very fast and even has an whobbling orbit ( the satellite altitude is not always the same ) i guess the people at inmarsat did a hell of a job what was never done before to calculate this arcs at all.
the initial search area was an assumption the flight path between the arcs was a straight line with the same speed at same altitude and the last partial ping represents fuel exhaustion and ( +-glide ) crash side .
but without knowing at what altitude that happened ( glide time, glide characteristic ) , with changing wind directions and so without knowing what exact flight path the aircraft took to reach the final seventh arc they have a hard time to say where the aircraft exactly is on this seventh arc.
best regards