Yes. The presumption in Quebec is that the marriage ceremony was carried out in good faith, therefor the burden of proof falls on the spouse trying to annul the marriage to prove that the marriage is void. Examples that give rise to annulment can include: the marriage ceremony was not performed by an authorised person, a marriage license was not obtained, one of the persons was too young or did not give her/his free consent etc.
! Note that religious annulment does not affect the legal validity of the marriage. Therefore, if legal annulment is sought, religious annulment will not make the marriage legally null.
For more information, please see http://www.justice.gouv.qc.ca/english/publications/generale/maria-a.htm
If you do not have legal proof of your marriage, you are not considered to be legally married in Quebec. You therefore have no ground to apply for your marriage to be annulled. Note that an annulment is distinct from divorce, because annulment establishes that the marriage never existed, whereas divorce recognises that the marriage once existed but that the marriage is now over. Grounds for annulment include bigamy, marrying a brother or sister, not following statutory procedure, errors in identity, and duress.
Alternatively, if you are seeking a divorce, you can ask the government of the place where your legal marriage occurred to reissue your marriage certificate, and which point you can apply for a divorce.
For more information, please see http://www.cic.gc.ca/english/resources/manuals/op/op02-eng.pdf