Hard to say exactly, but it's not crazy. But I doubt the difference is that large.

Diesel engines for locomotives are likely 40% efficient before accounting for the motor-generator section. A modern a coal fired power plant might be 40-45% efficient. So probably the same based on raw thermal numbers.

I suspect economically the electrification is a win.

Also over the future it's possible to run the electrified trains on electric power from greener sources, like solar and wind. Where diesel would require a big upgrade.

An electric train may require less energy because it doesn't need to move the engine along the track.

It also doesn't need to move the fuel it needs, either. Plus if cleaner fuel becomes available, it can switch as soon as it's hooked to the grid.

Correct. They can also return energy when braking, although it usually helps to have a decent density of trains running at the same time.

The Tesla fans can probably give you the details -- although they're still a little wedded to cars. A coal plant can use filtering much more elaborate than anything a private vehicle can use, so reportedly a Prius (35 MPG) has about the same emissions as a Tesla fueled from an all-coal grid.

I don't disagree with your general point (although I'll quibble a bit about non-carbon emissions; even heavily scrubbed coal emits a lot of heavy metals that aren't present in gasoline).

But what Prius only gets 35 MPG? Did you mean 53MPG? My old Prius with batteries that are getting long in the tooth still gets 40-45 MPG.