Store: Probably ok, but you’ll want to be sure the gantry is resting against blocks, resting against the lower plates in that case to take the load off the belts. If the belts have the extra tension of the gantry hanging on them, they might stretch and need recalibration. For that matter, keeping the base flat will take some care with how you support it - a little torque on it and it’ll be out of square with the spindle again.
The more I think about this, the more hassle it seems.
Run it: I think that’s going to have a lot of problems, and the spring tension in the Z axis is certainly going to be an issue to overcome.