Will the ceiling decay?
No, it shouldn’t.
There is no foundation or pillar to support it…are you sure?
I’m pretty sure a door on a foundation will reset the decay timer for anything built on foundation(s) connected to it. There is a foundation below it, since there are stairs there, and you have doors, so it should be fine.
Actually, that appears to be a ramp underneath it. But it is still connected to the foundation with the door on it.