Saxon was born aboard a space station in Syndicate space and he goes back there every once in a while.
I have to admit, though, it hasn't always ended well for him and one recent return trip was expedited by a particularly vicious gate ganking that left him sore even in the clone vat.
While Saxon and his family lived aboard the space station entirely, I also find it hard to believe that everyone would. As has been noted the resources required to do so would be epic.
I look at it kind of like this: The Gallente exiled the dissenting Intaki to an unsettled area of wild space and told them not to colonize the planets there. But the Gallente didn't do anything to enforce it. As far as I've seen there is no Gallente military or government presence in Syndicate Space.
So if the Syndicate Intaki were to start colonizing, but kept it covert, it would be difficult for the Gallente to know.
As for overcrowding, I'm not sure what the population of Syndicate Space is. Does anyone have a PF resource that details it?
I seem to remember reading somewhere that the initial Intaki exile population was about 5,000. I couldn't find a timeline that detailed when during the war they were exiled, but it couldn't have been more than 190 years ago.
Over the last 200 years, the Earth has averaged a 1.8 percent population growth annually. If the 5,000 Intaki exiles increased their population at the same rate for 190, they would now number just under 150,000. That does not take into account additional immigrants from other areas and their descendents since the exile, however.
Speaking of the new chron:
She waved dismissively at him and knelt slowly, pulling her long braid of synthetic blond hair behind her shoulder as she ran her hand across the concrete landing platform, tilting her head to examine her palm when it came back covered in a thin layer of dust and small pebbles. Smiling, she stood up and rubbed her hands together, nodding for the entourage to continue on their way to the cathedral’s spaceport terminal a short distance away. Despite the glaring sunlight reflecting off the glass paneled surface, she could see several figures anticipating her arrival near the main entrance.
As she led the group to the terminal, the last two armed escorts established positions near the ship, one of them leaning in closer to the other and whispering, "What was that all about?"
Not taking his gaze off of his responsibility, he whispered back, "It’s been a while for her."
This passage would make it seem that at least a few Syndicate Intaki spend the majority of their time in the sterile environment of a space station.