No... The logs don't say if someone uses voice chat, and even if it did, how can anyone prove what was said in voice chat?
You say the admins don't care, but if you don't record, they can't prove that anyone did anything wrong unless they were spectating the player for a whole 5 minutes prior to you being killed/robbed or whatever. How would you like it if the police came to your house and said, you're going to jail for 4 years and 2 months because Jimmy Bobworth said you robbed a gas station?
The reason videos people submit of him breaking rules don't work is because the evidence is most likely insufficient. The rule says that when you engage someone, you are engaged for 5 minutes, that means you need to submit an RDM report with 5 minutes of footage up to the point of death to prove that he did not engage you via voice chat. Text messages are logged but as I said above, voice isn't. Don't be fucking stupid and state that the admins don't care.