YES. If you receive a moving violation from a police officer (this does not include red light and speed enforcement camera violations as well as parking tickets), this will impact your insurance premium.
If you fight a ticket and the “points” are waived, you still have a rateable conviction on your driving record. Points are reserved for use by the Ministry of Transportation in Ontario. If you collect a certain number over a certain period, they can bring you in for a stern discussion or suspend your licence. Your insurer will not care if your points were dropped or lowered as you still have the conviction on your driving record.
A conviction goes on your driving record once you have been found guilty of the action (either by not challenging it or paying the fine) and remains on your abstract for three (3) years from that date, not the date of the offence. Most Canadian provinces and many of the USA states have a reciprocal arrangement with Ontario, so an out of province ticket may still appear on your Ontario driving abstract.