While it may be possible, it's not something I would want to do. I would prefer getting my bag and dropping it off the next day. If it were the first flight out the next morning I would trust them, but all day I would not be confident in them getting it on the flight.

You will need to pick up your bag to clear customs, so even if they do tag it all the way through make sure to pick it up and drop it off again if you don't want to hold on to it.