No. Unfortunately not possible since you are under a removal order and without status. It's not possible for refugee claimants or failed refugee claimants to apply through economic immigration programs from inside of Canada. You would only be able to do this if you left Canada.
If you filed a refugee claim, that puts you under a removal order automatically. That removal order is put on hold while you have the claim or any appeals in process. The OWP does not give you status in Canada. So unfortunately not feasible to apply for PR through EE or PNP.