That could be done. I would just have to select the random civs in my mod instead instead of letting the game code select random civs. The hard part would be coming up with something that would be interesting but not overly complicated. If filli_noctus (or anybody else) has any other ideas involving random civs - post them here and I'll put some thought towards adding something like this the the mod.
A couple of possible ideas:
1. Change the active check box to a percentage between 0% - 100%. 0% - the civ never shows up (same as inactive), 100% - the civ always has a chance of showing up (same as active). Otherwise the civ might show up with the chance increasing as the number gets higher.
2. Group civs by geographic location. North America, South America, Europe, Asia, Middle East, Africa etc... Then add those items to the civ selection list for each player. For example if the user selects "Middle East" for player 2 in the civilization select screen then a civ from the middle east would be randomly chosen for player 2 when the game starts.
If anybody has any new ideas or feedback to the ideas posted above by myself and filli_noctus feel free to post them.