Since he appears to still have a physical boundary I sadly have to stick with "no", like many of my foreposters.
Yes. He qualifies complete as a Warp entity, especially considering the Chaos Gods are stated to be omnipotent within the Immaterium, yet the GEOM while on the Golden Throne and being fed the souls of around 3,650,000,000 psykers has more or less rendered him a warp deity. Especially considering the rather weak Eldar gods qualified as gods, the GEOM most certainly qualifies as a warp god around the fortieth-forty first millennium. He certainly isn't the strongest however, but he's more or less ascended. The iffy thing however is that the Golden Throne isn't sustaining him most likely, considering his a perpetual, and thus what happens if he's kicked off would be very interesting.
Firstly, is it completely established that the Chaos Gods are truly omnipotent within the Immaterium? They have their own realms and boundries, but from the look of things there are still limits as to what they can manipulate. A certain Gray Knight is seemingly untouchable ( In the direct sense ). Secondly, I have my doubts about the GEOM's current state as a result of him devouring so many souls. It's pretty plainly stated that the souls are directly fed to him in order to power the Astronomicon aswell as giving him the strength to continue his struggle against the Ruinous Powers. We haven't exactly been privy to information stating that he's been getting stronger by all of this. If anything I'd compare him to an engine, you may supply new fuel each day before it runs dry, but the efficiency of the engine remains the same. Now wether the active worship by trillions of humans contribute to his presence in the warp is a completely different matter. In general, the 40K universe has never provided us with a strict way of measuring "divine" power. The C'tan or gods, the dead gods of the Eldar were gods, the powers in the warp are gods. Add to that beings such as Gork and Mork and the Hive mind... It's a mess alright.
I've figured it out. OP is a Chaos agent of change. There was no reason for him to ask such a question except to plant the seed of doubt in the unshielded mind.
Stated within the Chaos Daemons codex, either the 4th or the 5th, I'll have to check online. The thing really isn't his power, it's the fact that the title 'god' is thrown around in W40K so lightly it doesn't really have any worth. Is he a god? Yes, as much as the Eldar Gods were, if not greater- maybe even on par with an unshattered C'tan. Is he a fully omnipotent force capable of stomping the others into the dust? Not at all. He's more of the little dutch boy with his finger in the damn than he really is a shear force of power to cause the Chaos gods to run for the hills. However, combined with the devouring of pysker souls and trillions worshiping him, it's likely his power is increasing at a steady rate. However, it's simply hard to tell thanks to the Golden Throne. Which actually shouldn't be doing anything for him as life support. Unless Horus actually damaged his soul, the GEOM is easily capable of regenerating thanks to being a perpetual. Either he has to be on the Golden Throne as it amplifies his abilities and allows him to hold back the Chaos Gods, or the Golden Throne is actually detrimental and is imprisoning him and preventing the GEOM from taking control of his corpse-body again and rising off the throne.
Full C'tan, the original before they were shattered by the Necrons in their rebellion of the Silent King, were capable of creating black holes and dumping solar systems in them from what I've heard from Necron-player friends. They were pretty frightful apparently. Makes sense now why the Nightbringer put the fear of death into most of the galaxy.
Awesome points made in the posts above... Food for thought. I made an appropriate post in another thread, however, and I really don't want to go over all that again, so here - http://forum.eternalcrusade.com/threads/who-is-the-best-god-of-40k.1228/page-6#post-33054
Black holes? Ask 'em for citations. The most impressive thing I know about is the Orrery (which I semi-debunked on SB as not being universal but galactic in scale) and some vague reference to 'channeling the energies of the universe' into some superweapon to blow up the C'Tan.