I was setting up my Alpha at a rehearsal the other day, and started up Eigen D as soon as I could to get the long startup out of the way. I then realised I'd forgotten to turn on the base station, and thought I'd have to load EigenD again, but as it was it picked up the Alpha quickly and started running fine. This seems to imply that the long startup is purely loading things into memory on the host computer, not into any memory in the Alpha or the base station.
To further this experiment, I tried hibernating my MacBook with EigenD running, and it works for short hibernations, but if you leave it too long, then when the Mac wakes up, EigenD shows 'Stopped' instead of 'Running' and you are then forced to restart it or load a setup which puts you through the long startup again. Shouldn't EigenD survive hibernation indefinitely, and then connect to your Alpha once you plug in the base station and Alpha?
If this is easily achievable this would dramatically reduce setup time, since you could leave EigenD running permanently, and just wakae up your mac when you go on stage.