Is it possible to copy the output of a cell in the GTK notebook as TeX source?
Yes.
Cadabra version 1: The cadabra notebook file contains the $\LaTeX$ source of all your cells. You can even run $\LaTeX$ on it.
Cadabra version 2: Export your notebook as $\LaTeX$ source.
Thank you Konrad!
The feature is available in v.2.x since January 2018.