You can, technically, enter India with one passport and exit with another PROVIDED you have a long trip. To do this, you have to apply for something called an exit visa. In order to apply for an exit visa, you have to surrender your Indian passport.People keep thinking "Oh I can use Indian passport for 3 more months after getting citizenship" but totally forget the issue of how they will return back to Canada with no documents as your PR card will be gone. Two scenarios
1. If you do NOT get a Canadian passport, you may potentially travel to India with your Indian passport and citizenship certificate and apply for your first passport there, although not sure timelines to get a passport in India - especially the first one. Also the issue of entering on 1 passport and exiting with another is a no-no
2. If you do get a Canadian passport, then you need to surrender Indian passport COMPULSORILY and get an Indian entry visa before you fly. You cannot enter India with one passport and exit with another.
So, if you are planning to go to India for 2 - 4 months or more, then this option might be possible.
Travel to India on Indian passport > Apply for Canadian passport > Apply for exit visa and surrender of Indian passport > Fly back to Canada on Canadian passport (and show exit visa when leaving the country).
First of all, it takes time to obtain a Canadian passport in India AFAIK. After that, you'll have to surrender your passport and get your exit visa and that takes time as well. I don't know how long these things take so it is safe to assume it'll take a couple of months (bare minimum). It is very difficult to plan your trip around these procedures. That's why, it is safe to NOT travel to India on an Indian passport once you receive Canadian citizenship.