I thought they had it set to automatically open when they reach the other Galaxy.
It's been months since I watched the series finale so there is a strong possibility that I got it wrong, and that you are correct.
I know I am right about Eli having only 2 weeks worth of power and rations available to him, by which time, he should have either fixed the pod, or make the "sacrifice". If he doesn't, his continued use of life support means that Destiny would fall short of the next galaxy, meaning that there would not be enough power to keep the stasis pods going, meaning people would start dying inside them.