Do the bonus quests for Companions' leaders end?

No, these quests do not end. These are simply due to the Radiant A.I., and never ending quests.

Also, as the Harbinger, you're not the leader, it would be better described as an adviser to the council of Companions.

The Companions have not had a leader since Ysgrimor thousands of years before the game of Skyrim. Once Ysgrimor passed on nobody felt they could live up to Ysgrimor's title as Leader and thus was born The Harbinger. The harbinger is better described as a group advisor rather than a leader. As far as the quests, I have done at least 5 quests for each of the remaining "leaders" and I still get the quest. Everything I've read online says that there is no end to the quest. Hope this helps...