As a general rule, airlines will NOT let you board the initial flight if you do not have the documents for your entire trip.
There are a number of reasons for this, including the one you've mentioned - hidden city ticketing. Although you've stated that is not your intent, the airline isn't necessarily going to believe you!
However the bigger reason is one of immigration legislation. Ending your trip in the US changes the reason you are visiting the US (from transit to staying), which potentially changes your visa/status requirements there. In your case as you have a B1/B2 visa you can potentially enter the US without a return/onward ticket, but it still puts you at a higher risk of being denied entry, and as the airline will not have correctly enforced the visa requirements for your onward flight they will potentially be held responsible.
There is one exception to the above, which is that if your stay in the US is more than 24 hours then you will only be checked in to your destination in the US, and your documents will only be checked for that leg. This is because a stay of over 24 hours is a stopover, which means that you are legitimately planning to stay in the US (even if only briefly).
Your best bet is likely to contact the airline and change your flight to end in the US. There will likely be a fee involved in doing this, but it will depend on the exact fare and the agent involved. Given your US B1/B2 visa it's certainly possible you would be allowed board the flight to the US without the correct paperwork for Canada, but it would be unlikely.