Hi Hazelnuts.. you quote..
'An upward gust adds energy, increasing height at constant speed. '
I think you are 30% right. But that ignores the pitch up of the nose caused by the gust, which goes into adding the further 70% of the climb.
The nose of the plane then has to pitch down.. It does slightly too much, so it has to pitch up again, and again overshoots.. etc. ad infinitum.