This has been discussed in soft canon (where the answer has generally been yes the animating consciousness or what have you goes with the transporter beam) but examples of "transporter clones" have happened in hard ans soft canon (e.g.Thomas Riker), so I imagine that it depends on what the writer needs for a given story.
This question goes all the way back to the original series, and some of the first novels written for/about it. Just as the existence of souls is itself a matter of faith, not science, it can only be answered on those terms, and the answer is likely to be a personal one.
obviously cosciousness is a byproduct of our brians being configured the way they are seeing as how conciousness can be interputed or even removed all together by strokes and or brain trauma and leave use a veggie or even more or less brain dead if not brain dead.
So imho consiousness is somewhat linked to the idea of a soul but not entirely, and to state this I do believe in souls. I think it is much more likely that souls are both part of and seperate from you, more like an external harddrive, so when the primary eventually fails the external disconects and moves on with the total culmination of lifes experiences and in essence takes over where the body failed. And in the process of teleportation when one is atomized and reconfigured in the exact state it was dematerialized in the soul just follows the info to the new point and reintigrates, if it would ever not be integrated, cuz who is to say souls if they exist are not anywhere and everywhere at the same time, seeing as how the afterlife could work on completely diffrent physics if it worked on any kind at all.