Generally, yes. Things like suicide encouragement fall under "zero tolerance" language, and subsequently result in escalations past the standard progression in the vast majority of cases, if not every time. Based on my understanding of the system, it may (or may not) be more lenient if it's a single instance across dozens/hundreds of games, though that is mostly speculation based on information provided by Riot and what I've seen in certain cases. Generally, Riot will only be harsher on newer accounts if they can be identified as alternate accounts from users who've exhibited such behaviours previously (and mainly those who've previously been banned).
Worst comes to worst, you're looking at a 14-day ban, and if that happens it may just be a good idea to disable both "all" and "team" chat in the games options, if you think that's going to be effective for you.