Don't think a lot of members would show up. The clan world is a competitive world and most members want to know who won. It would be pointless to show up and lose sets while knowing there will be no clear winner. Fighting for the sake of fighting is a waste of time.
It's definitely true that people who clan or who continue to clan today are highly competitive and want to win and know who the clear winner of a fight is - I won't dispute that. In the sense of pure competition, a fight such as this would be pretty pointless.
On the other hand, I don't think it would be totally pointless because at the end of the day, OSRS and clanning are hobbies and something that most of us engage in purely for entertainment and fun. Weekly fights such as this would mean entertainment for 2 hours on a Sunday afternoon (or whatever day) before everyone is back at work/school/real life for the week, and I think people have seriously lost sight of the fact that beyond the entertainment factor, this whole OSRS/clanning thing is pointless in and of itself anyways. So, if having a cluster once a week provides a little fun, I'm all for it because at the end of the day, many clanners including myself are just looking for a fun activity to engage in during their spare time.