Short answer: Yes. You would have made it to a kiosk earlier, and had a few minutes to click the "check a bag" button.

As soon as the clock ticks over, the flight closes, and it's much more work (but certainly not impossible, as you stated) to get the bags checked.

But even ignoring the bag deadline, I don't understand why you weren't allowed to board at T-20, unless the original check-in agent had offloaded you, so they closed the doors after all checked-in passengers had boarded.