From your friend's experience with Extatosoma, we know that species of stick insect would not be an ideal species for George_Adams greenhouse. Other species have stricter diets, such as Oreophoetes topoense, that is only known to feed on species of fern. Experimentation would be in order before releasing stick insects upon any plants that could be at risk. However, George_Adams does not yet have a greenhouse, and proper plant selection could work around the chosen stick insect species.
So, would keeping stick insects in a greenhouse be possible? Absolutely! However, many details would need attention and it could involve a lot of work to maintain the stick insect culture long term.