It does look like it. However, somehow I think that the Coalition, although mainly gathered on and around Earth, should also have had its bases elsewhere in the Sol system, since they need a lot of resources for the fleet (e.g. minerals, metals, etc.) that are scarce on Earth. It's more like reasoning than statement of facts, though

I don't have a drinking problem. I drink. I get drunk. I fall down. No problem.
(stolen from a local pub)

Not sure where they are stationed at the beginning but I kind of got the feeling they had been massing their fleet for awhile considering how much damage they inflicted on the first strike.
I would assume they had a few planets which were resource rich, fuel etc. at the edges of the sol system or maybe just one area. Open for debate really.....

Skymouse

They may have had space-based bases?

Highly possible, but, if you remember the briefings, the attack started from Earth towards the outer sectors of the Sol system - at least that was the direction of the attack arrows.

I don't have a drinking problem. I drink. I get drunk. I fall down. No problem.
(stolen from a local pub)

I believe they occupy and exploit a varying degree of portion of each worlds, while the Alliance have the bigger slice. Perhaps it started out like some sort of non-violent space-race and resources exploitation and colonization by each independent nation. Minor skirmishes here and there forced the colonies to absorb themselves into a strong defense pact, and the defense pacts themselves annex to an even larger military cooperation, namely the Alliance and Coalition. I wouldn't be surprised if the Alliance colonies shared a ground border with the Coalition colonies on Mars, for example. Imagine America in its early years, colonized by French, British, Portuguese and Spanish powers. The colony settlements are polarized for defense and ancestral reasons, but the fact is: they are still in the same continent.

The Coalition hails from just about anywhere that was Communist during the Cold War. I don't know where their bases are concentrated, but If I had to take a stab in the dark, I'd have to say Saturn, since you hit a lot of their installations in Saturn space.

Reaper: $200,000,000.
Rockets: $100,000
The look on that pilot's face when you launch a full pod of screamers up his tailpipe: priceless

Correct me if I'm wrong, but wasn't the Czar being built in the orbit of Jupiter?