I feel like it's pretty unlikely that it's going to do so much damage that you have to evacuate, but it's hard to say without seeing the tree. It also depends on the structure of your house, too. I grew up with hurricanes and watched a pine tree fall on our house during one. It damaged the roof but not so disastrously that we had to leave.

You can find some articles online about what to do if it happens - who to call, what documents you need on hand, and other safety tips if it falls on a power line.

I'd just be prepared to keep everyone (especially your gecko!) warm. Having stuff set aside where it's easily accessible if there is extensive damage is not a bad move, either.