The answer depends on whether you were the one at fault in the motor vehicle accident.
If you were not at fault for the car accident, the insurance company cannot increase your premiums just because you claim no fault or accident benefits.
If you were at fault for the car accident your insurance company can in fact raise your premiums on you. They can do this because accidents, tickets and other blemishes on your driving record will increase your rate of incidents.
Other aspects that can affect your premiums are what kind of car you drive, what neighbourhoods you drive it in and the distances you drive.