No. If you are on implied status, meaning that you applied to extend your work permit prior to the expiry of your initial permit, you may continue to work under the same conditions of your original permit, even if your SIN is expired.
As soon as you receive your new permit, you can apply to renew your SIN.
If your SIN has expired and you are on implied status, and you require assistance explaining your legal work status in Canada to your employer or otherwise, please contact Toronto immigration and employment lawyers, Sultan Lawyers, at (416) 214-5111 or via email to mlahert@sultanlawyers.com.