It depends on how the H-1B petition was filed. I suspect that it was filed not with a request for change of status but with a request for consular notification

It depends on how the H-1B petition was filed. I suspect that it was filed not with a request for change of status but with a request for consular notification which means that after you get the waiver you will need to leave the US and apply for an H-1B visa at a US Consulate abroad.