Extending integrated carbon seat tube Can I just cut the carbon seat tube, cut a vertical slot for compression and use a conventional seat clamp to hold a seat post in it?
That is unlikely. The inside of a frame is machined/molded to a specific size for the seat post. An integrated post is not finished internally. Also, it is unlikely that the internal and external diameters of the post/frame/clamp would match well enough to be ridden safely.

Seat post fitting is a zero tolerance game, and they are dimension-ed to the tenth om millimeters. You would have to be beyond lucky for that to work out.