What happens to a human body when it's stabbed in the chest?
It looses information - it's composed of the exact same elements as before , but they're not ordered like before.
How does a transporter work?
First, it scans one on the quantum level (heinsemberg compensators), storing this information in the pattern buffer.
In DS9: Our man Bashir, it was this information that filled all hard-drives of the station - computer memory stores information, it's not a capacitor that stores energy.
Second, the body is 'dematerialised', its matter turned into some unspecified form of energy.
What is known about this 'energy' is that it can't hold the information necessary to build a human - it degrades rapidly (evidence in practically any episode dealing with transporter malfunctions). This is why the body needs to be scanned in the first place, in order to preserve the information that 'defines' a person'.
Third, the body is rematerialised, using the information stored in the pattern buffers.
Attention - the 'energy' degraded to a level at which, if it is 'rematerialised' without using information from the pattern buffers, the body transported is dead. This body lost information, the person died, regardless if the copy is composed of the same atoms or not.
What is rematerialised is a copy of the person. And, in TNG: Second chances, it is shown how more than one copy can be created.
Proto Avatar:
But your theory is wrong no matter how correct it sounds or makes sense. The transporter has never operated under this premise. Despite it's function it transports the original person. It might even be a contradiction in how it works even. But the fact of the matter is that it works like a car ride and doesn't kill a person and doesn't make a copy. No matter what pieces of information you try and stitch together and say.
However, the transporter can still operate under the information that we have been given from the series, though.
In other words: Your body doesn't die. It is simply converted into living energy where your physical pattern is waiting to be converted back. The energy state (i.e. neural patters) between de-materialization and re-materialization is simply alive during transport. Otherwise the Federation would have the power over what lives and what dies (by just using a person's DNA).
Simply put, the transporter cannot replicate life. It merely transforms and transports it. And to assume that you are dead during the energy process is just that. An assumption. Also, many energy beings exist within Star Trek. It is not illogical to think that the transporter wouldn't keep you alive during the process in some way. Even your physical body could still be alive but out of phase with our reality for a brief time until it is called back into the physical world using the right DNA key code (i.e. transporter pattern) to align it with our normal plane of existence.