Me thinks it has little direct influence besides as a political tool unless it is widely coordinated with other alliances. Some political developments would need to take place for it to be used on such a large scale, but that'd be interesting if it came about anyways.
On Color Senate: Maybe have the three largest alliances on a color have a vote that influences their color in some way related to economics, with later increasing that number as the game size increases.
Or have the votes within the colors be based on some other statistic besides overall strength, idk. Maybe total member count on a particular color in the same color alliance versus the same for the other same colored alliances. You'd have a majority vote if you basically controlled the whole color, but it'd be interesting either way.