The global ocean circulation adjusts on long time-scales and plays a fundamental role in the Earth climate system through how it impacts transport and storage of tracers such as heat, CO2, oxygen. On centennial to millennial time-scales, the mesoscale eddy feedbacks play a leading order role in how the global ocean circulation responds through its impact on the residual overturning circulation, i.e. the residual of the Eulerian overturning circulation, countered by the eddy induced overturning circulation. In such scenarios, how models represent mesoscale eddies often leads to a change in the global ocean circulation that is larger than the combined effect of other classes of parameterisations. Here we provide the first investigation of the geometrically informed, eddy energy constrained parameterisation framework GEOMETRIC in a global ocean configuration model, given the recent success of GEOMETRIC in being able to capture expected ocean circulation sensitivities in high resolution models with explicit eddies. On the one hand, we demonstrate that GEOMETRIC does indeed produce the sensitivities in the global circulation to changes in the Southern Ocean wind forcing, as expected. On the other hand, we show that changing the eddy energy dissipation magnitude results in significant changes in the Antarctic Circumpolar transport and Atlantic Meridional Overturning Circulation, leading to changes in the ocean heat content that is an order of magnitude larger than that normally found for climate change studies of the post-industrial period. The significant impact of eddy energy dissipation on global ocean circulation points to an urgent need to combine theoretical, modelling and observational efforts to constraint the associated uncertainties associated with eddy energy dissipation.