Very possible. My alloy post bonded solid into carbon frame. Hell of an effort to get it out and almost was going to cut it out. Tried all kinds of stuff, though I lacked a big vice to put the post in and rotate the frame as one trick is (not sure it’s wise with a carbon frame anyway).
What seemed to work best was soaking in some snowboard/ski base cleaner. Basically a citric acid fluid. I then started getting tiny movement with a lot of twisting force, and just kept trying to rotate it. Took hours, a lot of squealing noise and a hell of a lot of effort and swearing.
Now I don’t leave the post in the frame apart from riding. Also, coat the post surface with carbon assembly paste. It helps protect against this and also reduces the torque required when clamping carbon.
And yes, in my case the alloy corroded. Surface of the post was very corroded. Frame was good.