That's a bit exaggerated for a "nation", but surely not for a faction counting billions and billions of citizens.
I order to criticize the idea, you need to know quite a few things (time span, available technologies, how willing is the faction to do that, available resources, reasons behind that action, possible benefits, etc. etc.) and most of them haven't been mentioned. I think criticizing the idea a priori simply because at first it doesn't sound convincing is a bad approach.
On a side note, Mars was terraformed between 2100 and 2300, which is a plausible and to some degree even pessimistic time span. It is totally unrelated to both the GTA and the EA, as they emerged later: things were already that way, so the EA's only great achievement in terms of terraforming was the Moon.