I was playing a modded game of GalCiv 2 last night and discovered for myself what happens if you rush too many colonies too soon. I ended up 2000bc in the red with a shrinking approval due to prolonged debt, and having to keep taxes low enough to keep approval hovering at about 50%, with just enough income to eventually get out of the red.
I managed that after snagging 25 colonies but not researching far enough to get any economic buildings.
Thing is, this can happen to the AI as well. There are a few races that don't get, for example, the basic Market improvement, I know because I was playing one of them.
Endless Space actually has a fairly steep approval penalty for expansion, but like GalCiv it has technologies and buildings to combat low approval. Similarly, Civ 5 has unhappiness relating to number of cities and population.
I'm not sure where GalCiv 3 will go with it's approval model, but no doubt it will figure somewhere in how fast you can expand, even if there isn't a per-colony hit on approval.