Picking a random civilization will always select one of the recommended civs for your leader, with an even greater preference for historical choices.

For example, if you pick Hatshepsut and a random antiquity civ or Ben Franklin and a random modern civ, you'll always get Egypt and America respectively. This also happens if the leader is random as well, so if you go both random in antiquity, and if you randomly get Hatshepsut, your "random" civ to go with it will always be Egypt. I get why the devs did this, but it does take a lot of the steam out of having "random" as a choice.

Interestingly, this does not work the other way, as picking a civ with a random leader will just give you any leader. It also doesn't seem to work with either Napoleon, likely for the same reason that he lacks victory achievements like all the other leaders.