score:5
As stated by Timatic, the database used by airlines:
Visa required, except for Passengers with a British passport with nationality of British Citizen shown on the bio-data page. The passenger must have an Electronic Travel Authorization (eTA).
If ground staff lets you board, the airline will be heavily fined and could lose its licence to fly to Canada. What's more, they'll likely make you pay their costs and could ban you from flying with them again.
As you may guess, there's no way they'll take this risk.
So don't even waste time thinking about this. Wait for the ETA approval, and then get a new ticket as cheaply as you can.
Upvote:5
Clearly the situation of the original poster has now been resolved one way or another. However, for the benefit of others in a similar situation here is some relevant information:
In my case, having attempted to check in the day before an early-morning flight to Canada, I had the situation resolved before leaving home -- a 5-hour delay, but I was able to catch the intended flight with my family.