If I log out while inside a Thargoid base/structure...

[mp4x]

(prior to the update)
And log back in on the 27th of September, do you suppose I'll see any changes inside?

 

[Conch]

you will become one of them!

 

[Sitoutumaton]

Sadly, this is not possible. The game will not let you log out in the crater of a Thargoid base. I tried and the game told me to move to safer location first.

Forced log out might just deposit you outside the "danger zone".