Assuming that there is no "soul" or extra entity that makes you "you" not already defined by modern physics...
Even if there were such a thing as a soul, it would not necessarily exclude that possibility. It maybe that the 'soul' can bind itself to the result of the teleportation just as it did to the original.
Let's take for example Rupert Sheldrake's concept of morphogenetic resonance which is, although a piece of crock, a fascinating idea. If this 'theory' were correct, it would make teleportation even less problematic than it is in a strict materialist universe. Because the person stepping out of the receiver is so much like the person who stepped into the transmitter, s/he will resonate very strongly with the morphogenetic field of the person who stepped into the transmitter. The person at the receiving end will simply have all the memories and the same conciousness, soul if you will. That's true even if that person is not a perfect duplicate of the first, the only thing that matters is that s/he is alike enough to resonate strongly with the original.
How about this for a teleportation experiment:
Suppose you are led into a room, which is unbeknowst to you actually the inside of a teleporter. Without you noticing the teleporter makes a perfect copy of you in an identical room, but does not destroy your orginal. So there are now two identical yous, in two identical rooms. How long will it take before the two yous start behaving noticably different?
If your conciousness depends at its deepest level on quantum randomness, the behaviour patterns of both yous start to divert fairly rapidly. And both end up as two different people.
On the other hand, if the universe is ultimately deterministic, both yous may behave very similarly for a long time. After a while though, even the smallest differences between the rooms will have 'butterfly' effects, and slowly but surely, the yous start differing in behaviour.
In a Sheldrakian universe however, both yous will very strongly resonate morphogenetically. The rooms and the two yous are so similar that they influence eachother making sure behaviour stays the same. Even if the yous are lightyears away from eachother, there is no observable difference between them. Whatever small difference there may be, it will disappear through mutual influence. You have not split in two, but in a way you also do not exist in two places at once, because the even rooms are identical and resonate with eachother making them basically one and the same room. Distance ceases to exist.
