Does anyone know if the admissions committee even know or care if you have participated in the write-on competition at their school before application is reviewed? In the rare scenario that the applicant would have qualified for LR through the write-on, does that get taken into account during application review? I'm debating whether I want to do this beastly write-on competition on top of my current school's write-on competition.
Maybe. But I'm not sure it'd help you.
I would imagine that "likelihood to attend if accepted" is a relevant factor in their decisions. If you took the time to participate in the write-on, it may help you there. But I wouldn't be surprised if coming off like a weirdo with too much time on your hands would hurt you more.
If you do participate, make sure you had great grades this semester. Otherwise they might think you suck at prioritizing your time.