No you cannot / should not stay that way.
Implied status is basically if you applied for a permit extension OF THE SAME TYPE that you were on already (e.g. if you were already on a work permit and you applied for an extension BEFORE the expiry of permit but your renewal hasn't been received YET. So you continue working until CIC passes a judgement on your application.
That is implied status.
If your current permit expires and you haven't applied for any extension then basically the only option is to apply for restoration of status with in 90 days with a special fee, among other requirements.
The only way i know you could stay for another 3 months (of course without getting a work permit) is getting a visitor trv and stay for that long.