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Generally, no. The use of a credit card is also used as a credit check to confirm the consumers credit risk.
I would say, give it a try. Each account is different, but I have upgraded my phone using my debit card through the Telus site before, but I did it while signed into my account. It has been a while though since I have used the online system to upgrade a phone though. My 2 S9 Plus devices were both done in-store, so it was more than likely around a couple of years ago.