Yes, it counts against you more than anyone else.
It’s essentially cry bullying and even if you successfully got more people to report the player, that would not change the outcome. Lets be clear, you should report a toxic player because they will get punished if they continue their behavior. However, 9 reports in one game make little difference because it’s about the instances of toxic behavior more than it being witnessed by lots of people.
If that does not make sense, allow me to give an example. One day you steal a candy bar from a store. You are caught and forced to give the candy back and maybe fined etc. On the other hand if 10 million people see you steal the bar should your punishment change? Yes the court of public opinion can be ridiculous and cruel but should it really effect your punishment? I think Riot tries to avoid that for the sake of the average players as much as possible and it’s one thing that they get right.
In my experience the majority of players that spam all chat with report requests are already being toxic. Asides from the requests to report someone, these players tend to also be toxic in the usual way too. Any time I play I largely ignore chat and play my best and to have fun but anytime something goes slightly wrong there’s a chance someone will lose their schnitzel and be spamming chat about me. I don’t mind very much, on the contrary usually I find it amusing because I think it proves a lot of stereotypes about the community.
I have met so many players in denial about their toxicity (as well as their skill level) that it has become a joke. Don’t be that guy honestly. When you rage at someone else’s stupidity you do become toxic and though its understandable, it is still toxic. I have always said that you should just ignore a ‘Troll’ and the same applies to extremely toxic players. If you want to report them then go for it.
Riot Husker’s clarification
So I myself was not sure how seriously Riot took calling others to report players but apparently they recognize the issue. 6 months ago Husker responded to a thread asking for clarification on calling for reports here. He makes it clear that it is viewed as harassment and players should be reminded that it is itself toxic behavior.
There is more so follow the link and check it out if you’re interested but long story short, if you do this, stop it. Bad summoner. BAD.