In computer programming there's something known as the metadata, which is commonly defined as "data about data".
Thence I'd logically conclude that a transporter can beam itself, since this is explained by the metadata handling lesser units of data.
But that's software. You still need intact hardware to run it on. How the hell can a dissociated cloud of atoms function as a transporter?
Judging by what's seen in Voyager's "counterpoint" all the hardware you need to rematerialise people are a couple of projectors you install on the floor. These might as well be holographic? (thus software..)