I’d like to think I would, but given the circumstance, if I was just a civillian on board one of the ships, I might not know enough about Adama and gang at that point to trust them and risk everything on something and someone I know nothing about.
Adama and Roslin ran a tightlipped ship, so who knows what kind of rumours are spread outside of the Galactica? Especially after the whole Gaeta/Hatch thing. Adama and Roslin are good leaders, but they’re not the most transparent either - which led to things like the Gaeta/Hatch revolt.
So yeah. I hope I would. 