Unfortunately, YES.
That's what Iran is seeking.
SA never wanted (in the past) / never wants (right now) Yemen to enter a civil sectarian war.
Yemen demography comprise :
60% Sunnis
35% Yazidis (very moderate Shias)
5% Houthis (an estimation, I am not sure)
Houthis (Yemeni version of Iranian Shia Mullahs) are a minority in the minority (Yazidis), despite they are working to grow their followers amongst Yazidis.
SA used to have a very close relation with Yazidis, it -even- supported them in the 60' civil war against communists, cause they are not fanatics LIKE Iranian Shias and All Sunnis scholars consider them a branch of Sunni sect/faith despite very little differences.
I even can take you further on this point, Sunnis and even Salafis Clerics/scholars, use many books written by Yazidis Clerics/scholars in their teachings.
SO, now I don't know what Evil Sectarian IRAN wants from Yemen ?
Another Sectarian war like Syria and Iraq ? and then says it is Iranian Influence ?
Btw, did you read the post where I tagged you in the thread : Balance of power tips toward Iran (page 20) ?