Can you elaborate what you mean by provincial conviction? Are you talking about provincial traffic courts??
If the above is your concern, there is absolutely nothing to worry about as it is not considered "incriminating", however, if it's a DUI (which is a criminal offence under the Canadian criminal code), you might be looking at a possible cancellation/rejection of your PR application. Like i said earlier, if it's just ordinary traffic violation, like speeding, red light etc., it won't be considered a red flag.