The thermal characteristics of your glazing materials are the primary drivers determining performance. The fact that a geodesic dome has a somewhat different geometry and a somewhat different volume to surface area ratio, compared to a conventional greenhouse, is not going to make a significant difference in your situation.

unless it's a Growing Spaces dome!

I've seen the Growing Spaces GH Dome web site, and what makes their domes energy efficient are things like photovoltaic panels, sidewall and floor insulation, in-ground heating pipes, water tank for heat storage, etc. These are all things you can do to improve how a conventional GH works, and are not unique to a geodesic dome. Further, the design of a geodesic dome means that there is a chunk of growing space high up that probably won't be utilized, but will still need to be heated. Overall I think the Growing Spaces concept is good...it's just not magic that results from the shape of the structure.