The current TAS (with no L+R) can be found here:
https://www.youtube.com/watch?v=tdMHOXRX08o&t=0s
For the uninitiated, it represents a theoretically perfect speedrun where someone manually enters the exact required inputs for each individual frame.
It hasn't been beaten in over a decade, and RTA speedruns are inching closer and closer to this "optimal" time: the current world record ties the TAS in all levels except the last one, largely thanks to the so-called framerule system.
This resolves YES iff a (non L+R) TAS, generally accepted to be legitimate, is published to TASvideos, Youtube or some other public website which completes the original Super Mario Bros in strictly less time than the current TAS posted above.
I would recommend specifying the category somewhat more precisely; I assume you don't mean for the PAL version TAS to count? https://www.youtube.com/watch?v=9Iwnw8td97o