Dear FunkyFingers,
I currently work full time at a BK and my Brother is a manager at a different location. Basically if you don't watch the videos you are in the kindest way to put it... fucked.
I asked my brother on your behalf and he said "In my experience if a new recruit hasn't watched the basic training videos it is very obvious but we never have to worry about it as we usually let them go before the end of their first week.".
In my experience it is the exact same way at my location. Just push through the videos and learn, if you worked hard enough to get hired you should be willing to put some effort in learning the job it self. Remember working is a privilege, not a right. Trust me skimming through the videos isn't enough to get past.