Finally got through BLS call centre, agent advised if I travel with Indian passport, I will have to pay a penalty/fine later when I surrender passport.
Agent also said passport surrender process and visa/OCI application is independent. I have to do both, but OCI will be processed in 5-7 weeks and won’t be delayed awaiting passport surrender process.
Yes, you can leave Canada with your Indian passport without issues. However, you can't come back to Canada without a Canadian passport. You can carry your citizenship certificate and apply for a Canadian passport in India. However, my comment was about entering the country with one passport and leaving with another.
What you can do is this (this was posted somewhere on the forum and pointed out to me by a friend of mine).
Travel to India on Indian passport > Do NOT reveal about your citizenship > Apply for a Canadian passport > Get a visa to Dubai on your Indian passport > Exit India with your Indian passport > On arrival in Dubai, show your Canadian passport and get a visa on arrival > Book a ticket from Dubai to Toronto (or any other Canadian airport) > Show your Canadian passport when leaving Dubai > Come back to Canada.
Once you are in Canada, you have to pay a penalty to surrender your Indian citizenship and can then apply for OCI.