No. The designation by Revenue Canada is what opens the door to tax deductible donations.
We have had some donations over the years despite not being able to provide donation receipts. I am not up on the latest rules for donations but the write-off is not that significant. I believe it is on the order of 17 percent or at least was a few years ago.
Any non-profit and even for profit can receive donations without tax donation receipts. In Quebec, a for profit used clothings store posted a sing indicating that they accept donations. In order to save their reputation, they have teamed with legitimate charities. Some persons were gullible and fail to realize that they were giving to a for profit corporation.