Episodes like "Realm of Fear" where people are shown being active and interactive while within the transporting process are a clear-cut indication that you don't die in that machine. Or at least your death won't cause any sort of a discontinuity you should be worried about - unless you are a seriously sick person (like those who think elevators or mirrors or people named Jessup will be their inevitable undoing) and therefore are seriously incapacitated by your existential fears in the everyday environment.
Funnily enough, we can retroactively establish that the transporter was always like that, in (and especially in) TOS already. After all, a key element of the transporting process is that a person dematerializing in spot A will always
rematerialize in a different
pose in spot B. This is because of the method of trick photography used, which involves the actor walking to set B and taking a pose that closely but not exactly
approximates the one he held on set A. So clearly, the person inside a transporter beam is "in existence" the whole time, and acts and interacts so that his body can assume new poses.