If subspace radio can be believed to deliver real time messages and conversations across vast distances (even at warp), then it's not much of a stretch to think some kind of Trek technology could possibly be used to transport animate objects across just as vast a distance.
The issue for me is the amount of data. Admittedly, TNGadded layers of technobabble to the process but you need a beam of energy to prevent too much data leaking and you need heisenberg compensators to recombine the person successfully. It's hard to see how all that can still work at such long distances without a receiving pad if you can't even beam people out of the katric arc underground or when people are moving (FYI - the universe is moving, the planets are moving, the spaceships are moving, and tiny movements are magnified over long distances - it really should be a lot harder doing this over such long distances.
God-like alien tech aside, I can only see this working if they have a network of transporter relays on subspace communication relays to buffer the signal but transportees could end up being stranded if one of the relays is destroyed...
Or the Stargate style, where you open a wormhole and scan beyond it before sending the transporter signal through.
Now Stargate had a very good grasp on the limits of its tech and used it in some very effective stories. Trek tech is more versatile but I do wish the writers had a bible of do's and don'ts to work with.
Transporting over 20 light years would be on my don't list.