May I ask why you see the potential to get yourself banned? Do you have a hard time controlling yourself, or are you just scared of the system?
If it's the first, it's probably a good idea. If it's the second, followup question: Have you received punishment before? If no, I'd try without ignoring.
Maybe your behaviour is in line... and unless you go around exhibiting extremely toxic behaviour, your first punishment will merely be a chat restriction.
At that point you can then either see what you need to improve, or you can go ahead with the original plan.
As for whether ignoring can get you banned: "Ignoring" as in use the ignore function and/or simply ignoring what they type in chat? No.
Permanently going solo, ignoring pings, objectives and team fights is a bit more risky.
Edit: As Nami said, ignoring people that are bugging you is never a bad idea. Using the mute button is a good solution to a lot of problems.